Abstract
Numerical calculation from the full differential equations for convection in an unbounded region is expensive, and hence approximate solutions are important. For small values of the Rayleigh number Ra, perturbation methods are appropriate. At large values of Ra thermal boundary layers are formed, and boundary-layer theory is the obvious method of investigation. This approach forms the subject of much of this chapter. We follow to a large extent the discussion by Cheng (1985a), supplemented by recent surveys by Pop and Ingham (2000, 2001) and Pop (2004).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abbas, I. A. 2008 Combined effect of thermal dispersion and radiation on free convection in a fluid saturated, optically thick porous medium. Forsch. Ingen. Engng. Res. 72, 135–144. [5.1.7.3]
Abbas, I. A., El-Amin, M. F. and Salama, A. 2009 Effect of thermal dispersion on the free convection in a fluid saturated porous medium. Int. J. Heat Fluid Flow 30, 229–236. [5.1.7.3]
Abdel-Gaied, S. M. and Eid, M. R. 2011 Natural convection of non-Newtonian power-law fluid over axisymmetric and two-dimensional bodies of arbitrary shape in fluid-saturated porous media. Appl. Math. Mech. (English ed.) 32, 179–188. [5.9]
Abdelkhalek, M. M. 2008b Radiation and dissipation effect on unsteady MHD micropolar flow, past an infinite vertical plate in porous medium with time dependent suction. Indian J. Phys. Proc. Indian Assoc. Cult. Sci. 82, 415–434. [5.1.9.2s]
Abel, M. S., Mahesha, N. and Malipatel, S. B. 2011 Heat transfer due to MHD slip flow of a second-grade liquid over a stretching sheet through a porous medium with non-uniform heat source/sink. Chem. Engng. Commun. 198, 191–213. [5.1.9.9]
Abel, M. S., Nandeppanavar, M. M. and Malipatil, S. B. 2010a Heat transfer in a second grade fluid through a porous medium from a permeable stretching sheet with non-uniform heat source/sink. Int. J. Heat Mass Transfer 53, 1788–1795. [5.1.9.9]
Abel, M. S., Nandeppanavar, M. M. and Malkhed, M. B. 2010b Hydromagnetic boundary layer flow and heat transfer in a fluid over a continuously moving permeable stretching surface with nonuniform heat source/sink embedded in fluid saturated porous medium. Chem. Engng. Commun. 197, 633–655. [5.1.9.9]
Abou-zeid, M. Y. 2011 Magnetohydrodynamic boundary layer heat transfer to a stretching sheet including viscous dissipation and internal heat generation in a porous medium. J. Porous Media 14, 1007–1008. [5.1.9.9]
Abu-Hijleh, B. A. K. 2001a Natural convection heat transfer from a cylinder covered with an orthotropic porous layer in cross-flow. Numer. Heat Transfer A 40, 767–782. [5.12.3]
Afazal, N. and Salam, M. Y. 1990 Natural convection from point source embedded in Darcian porous medium. Fluid Dyn. Res. 6, 175–184. [5.8]
Afifi, A. A. 2007b Effects of variable viscosity on non-Darcy MHD free convection along a non-isothermal vertical surface in a thermally stratified porous medium. Appl. Math. Modell. 31, 1621–1634. [5.1.9.,9]
Afzal, N. 1985 Two-dimensional buoyant plume in porous media: higher-order effects. Int. J. Heat Mass Transfer 28, 2029–2041. [5.10.1.1]
Ait Saada, M., Chikh, S. and Campo, A. 2007 Natural convection around a horizontal solid cylinder wrapped with a layer of fibrous or porous material. Int. J. Heat Fluid Flow 28, 483–495. [5.5.1]
Al-Harbi, S. M. 2005 Numerical study of natural convection heat transfer with variable viscosity and thermal radiation from a cone and wedge in porous media. Appl. Math. Comput. 170, 64–75. [5.3, 5.8}
Ali, M. E. 2007 The effect of lateral mass flux on the natural convection boundary layers induced by a heated vertical plate embedded in a saturated porous medium with internal heat generation. Int. J. Therm. Sci. 46, 157–163. [5.1.9.4S]
Al-Nimr, M. A. and Massoud, S. 1998 Unsteady free convection flow over a vertical flat plate immersed in a porous medium. Fluid Dyn. Res. 23, 153–160. [5.1.9.9]
Al-Odat, M. Q. 2004a Nonsimilar solutions for unsteady free convection from a vertical plate embedded in a non-Darcy porous medium. Int. Comm. Heat Mass Transfer 31, 377–386. [5.1.7.2]
Al-Odat, M. Q. and Damseh, R. A. 2008 Viscous dissipation and joule heating effects on transient non-Darcy magnetodynamic convection flow of micropolar fluids past a vertical moving plate. J. Porous Media 11, 85–100. [5.1.9.2]
Angirasa, D. and Peterson, G. P. 1997b Natural convection heat transfer from an isothermal vertical surface to a fluid saturated thermally stratified porous medium. Int. J. Heat Mass Transfer 40, 4329–4335. [5.1.4]
Angirasa, D. and Peterson, G. P. 1998a Upper and lower Rayleigh number bounds for two-dimensional natural convection over a finite horizontal surface situated in a fluid-saturated porous medium. Numer. Heat Transfer A 33, 477–493. [5.2]
Angirasa, D. and Peterson, G. P. 1998b Natural convection below a downward facing heated horizontal surface in a fluid-saturated porous medium. Numer. Heat Transfer A 34, 301–311. [5.2]
Attia, H. A. 2006a On the effectiveness of uniform suction and injection on unsteady rotating disk flow in porous medium with heat transfer. Comput. Mat. Sci. 38, 240–244. {5.2]
Attia, H. A. 2006b Rotating disk flow in a porous medium. J. Porous Media 9, 789–798. [5.2]
Attia, H. A. 2006c Unsteady flow and heat transfer of viscous incompressible fluid with temperature-dependent viscosity due to a rotating disc in a porous medium. J. Phys. A 39, 979–991. [5.2]
Attia, H. A. 2007a On the effectiveness of porosity on stagnation point flow towards a stretching surface with heat generation. Comput. Mat. Sci. 38, 741–745. [5.1.9.9]
Attia, H. A. 2007b On the effectiveness of porosity on stagnation point flow with heat transfer over a permeable surface. J. Porous Media. 10, 625–651. [5.1.9.9].
Attia, H. A. 2008a Rotating disk flow and heat transfer through a porous medium of a non-Newtonian fluid with suction and injection. Comm. Nonlinear Sci. Numer. Simul. 13, 1571–1580.
Aziz, A., Khan, W. A. and Pop, I. 2012 Free convection boundary layer flow past a horizontal plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms. Int. J. Therm. Sci. 56, 48–57. [5.2]
Badruddin, I. A., Zainal, Z. A., Narayana, P. A. A., Seetharamu, K. N. and Siew, L. W. 2006b Free convection and radiation characteristics for a vertical plate embedded in a porous medium. Int. J. Numer. Meth. Engng. 65, 2265–2278. [5.1.9.4]
Badruddin, I. A., Zainal, Z. A., Narayana, P. A. A., Seetharamu, K. N. and Siew, L. W. 2006c Free convection and radiation for a vertical wall with varying temperature embedded in a porous medium. Int. J. Therm. Sci. 45, 487–493. [5.1.9.4]
Bagai, S. 2003 Similarity solutions of free convection boundary layers over a body of arbitrary shape in a porous medium with internal heat generation. Int. Comm. Heat Mass Transfer 30, 997–1003. [5.9]
Bagai, S. 2004 Effect of variable viscosity on free convection over a non-isothermal axisymmetric body in a porous medium with internal heat generation. Acta Mech. 169, 187–194. [5.9]
Bakier, A. Y. and Mansour, M. A. 2007 Combined of magnetic field and thermophoresis partical deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium. Thermal Science 11, 65–74. [5.1.9.9]
Bakier, A. Y., Mansour, M. A., Gorla, R. S. R. and Ebiana, A. B. 1997 Nonsimilar solutions for free convection from a vertical plate in porous media. Heat Mass Transfer 33, 145–148. [5.1.9.4]
Banu, N. and Rees, D. A. S. 2000 The effect of inertia on vertical free convection boundary layer flow from a heated surface in porous media with suction. Int. Comm. Heat Mass Transfer 27, 775–783. [5.1.7.2]
Bassom, A. P. and Rees, D. A. S. 1995 The linear vortex instability of flow induced by a horizontal heated surface in a porous medium. Quart. J. Mech. Appl. Mech. 48, 1–19. [5.4]
Bassom, A. P. and Rees, D. A. S. 1996 Free convection from a heated vertical cylinder embedded in a fluid-saturated porous medium. Acta Mech. 116, 139–151. [5.7]
Bassom, A. P., Rees, D. A. S. and Storesletten, L. 2001 Convective plumes in porous media: The effect of asymmetrically placed boundaries. Int. Commun. Heat Mass Transfer 28, 31–38. [5.10.1.1]
Beg, O. A., Takhar, H. S., Soundalgekar, V. M. and Prasad, V. 1998 Thermoconvective flow in a saturated, isotropic, homogeneous porous medium using Brinkman’s model – numerical study. Int. J. Numer. Methods Heat Fluid Flow 8, 559–589. [5.1.7.1]
Beg, O. A., Zueco, J. and Takhar, H. S. 2008b Laminar free convection from a continuously-moving vertical surface in thermally-stratified non-Darcian high-porosity medium: Network numerical study. Int. Comm. Heat Mass Transfer 35 810–816. [5.1.9.9]
Beg, O. A., Zueco, J., Takhar, H. S., Beg, T. A. and Sajid, A. 2009e Transient nonlinear optically-thick radiative-convective double-diffusive boundary layers in a Darcian porous medium adjacent to an impulsively started surface; Network simulationsolutions. Comm. Nonlinear Sci. Numer. Simu. 14, 3856–3866. [9.2.1]
Bejan, A. 1978 Natural convection in an infinite porous medium with a concentrated heat source. J. Fluid Mech. 89, 97–107. [5.11.2]
Bejan, A. 1984 Convection Heat Transfer, Wiley, New York. [1.1, 4.1, 4.2, 4.5, 4.17, 5.1.4, 5.11.1, 6.9.2, 7.1.1, 7.1.2, 7.3.3, 7.4.2, 9.2.1, 10.1.2]
Bejan, A. 1990b Optimum hair strand diameter for minimum free-convection heat transfer from a surface covered with hair. Int. J. Heat Mass Transfer 33, 206–209. [5.13]
Bejan, A. and Anderson, R. 1981 Heat transfer across a vertical impermeable partition imbedded in a porous medium. Int. J. Heat Mass Transfer 24, 1237–1245. [5.1.5, 7.3.1]
Bejan, A. and Anderson, R. 1983 Natural convection at the interface between a vertical porous layer and an open space. ASME J. Heat Transfer 105, 124–129. [5.1.5]
Bejan, A. and Poulikakos, D. 1984 The non-Darcy regime for vertical boundary layer natural convection in a porous medium. Int. J. Heat Mass Transfer 27, 717–722. [5.1.7.2]
Belhachmi, Z., Brighi, B. and Taous, K. 2000 Similarity solutions for a boundary layer problem in porous media. C. R. Acad. Sci. II B 328, 407–410. [5.1.9.1]
Belhachmi, Z., Brighi, B. and Taous, K. 2001 On a family of differential equations for boundary layer approximations in porous media. Europ. J. Appl. Math. 12, 513–528. [5.1.9.1]
Belhachmi, Z., Brighi, B., Sac-Eppe, J. M. and Taous, K. 2003 Numerical simulations of free convection about a vertical flat plate embedded in a porous medium. Comp. Geosci. 7, 137–166. [5.1.9.1]
Bhattacharyya, S. and Singh, A. K. 2009 Augmentation of heat transfer from a solid cylinder wrapped with a porous layer. Int. J. Heat Mass Transfer 52, 1991–2001. [5.5.1]
Boutros, Y. Z., Abd-El-Malek, M. P., Badran, N. A. and Hassan, H. S. 2006 Lie-group method of solution for steady two-dimensional boundary-layer stagnation-point flow toward a heated stretching sheet placed in a porous medium. Meccanica 41, 681–691. [5.1.9.9]
Bradean, R., Heggs, P. J., Ingham, D, B, and Pop, I. 1998a Convective heat flow from suddenly heated surfaces embedded in porous media. Transport Phenomena in Porous Media (eds. D. B. Ingham and I. Pop), Elsevier, Oxford, pp. 411–438. [5.5.1]
Bradean, R., Ingham, D. B., Heggs, P. and Pop, I. 1997b Unsteady free convection adjacent to an impulsively heated horizontal circular cylinder in porous media. Numer. Heat Transfer A 31, 325–346. [5.5.1]
Bradean, R., Ingham, D. B., Heggs, P. J. and Pop, I. 1995a Buoyancy induced flow adjacent to a periodically heated and cooled horizontal surface in porous media. Int. J. Heat Mass Transfer 39, 615–630. [5.2]
Bradean, R., Ingham, D. B., Heggs, P. J. and Pop, I. 1996 Unsteady free convection from a horizontal surface embedded in a porous media. Proc. 2nd European Thermal-Sciences and 14th UIT Nat. Heat Transfer Conference, Edizioni ETS, Pisa Vol. 1, 329–335. [5.2]
Bradean, R., Ingham, D. B., Heggs, P. J. and Pop, I. 1997a The unsteady penetration of free convection flows caused by heating and cooling flat surfaces in a porous media. Int. J. Heat Mass Transfer 40, 665–687. [5.1.9, 5.2]
Brambles, O. J. and Rees, D. A. S. 2007 Curved free convection plume paths in porous media. IDOTARAS 111, 109–122. [5.10.1]
Chamkha, A. J. 1996 Non-Darcy hydromagnetic free convection from a cone and a wedge in porous media. Int. Comm. Heat Mass Transfer 23, 875–887. [5.8]
Chamkha, A. J. 1997a Solar radiation assisted natural convection in uniform porous medium supported by a vertical flat plate. ASME J. Heat Transfer 119, 89–96. [5.1.9.4]
Chamkha, A. J. 1997c Similarity solutions for buoyancy-induced flow of a power-law fluid over a horizontal surface immersed in a porous medium. Int. Comm. Heat Mass Transfer 24, 805–814. [5.2]
Chamkha, A. J. 1997d Hydromagnetic flow and heat transfer of a heat-generating fluid over a surface in a porous medium. Int. Comm. Heat mass Transfer 24, 815–825. [5.1.9.4]
Chamkha, A. J. 1997e Hydromagnetic natural convection from an isothermal inclined surface adjacent to a thermally stratified porous medium. Int. J. Engng. Sci. 35, 975–986. [5.3]
Chamkha, A. J. 1997g MHD-free convection from a vertical plate embedded in a thermally stratified porous medium with Hall effects. Appl. Math. Modelling 21, 603–609. [5.1.4]
Chamkha, A. J., Aly, A. M. and Rahman, M. M. 2010c Unsteady natural convective power-law fluid flow past a vertical plate embedded in a non-Darcy porous medium in the presence of a chemical reaction. Nonlinear Anal. Modell. Control 15, 139–154. [5.1.9.9]
Chamkha, A. J., Issa, C. and Khanafer, K. 2001 Natural convection due to solar radiation from a vertical plate embedded in a porous medium with variable porosity. J. Porous Media 4, 69–77. [5.1.9.4]
Chamkha, A. J., Issa, C. and Khanafer, K. 2002 Natural convection from an inclined plate embedded in a variable porosity porous medium due to solar radiation. Int. J. Therm. Sci. 41, 73–78. [5.3]
Chamkha, A. J., Jaradat, M. and Pop, I. 2004 Thermophoresis free convection flow from a vertical cylinder embedded in a porous medium. Int. J. Appl. Mech. Engng. 9, 471–481. [5.7]
Chamkha, A., Gorla, R. S. R. and Ghodeswar, K. 2011 Non-similar solution for natural convective boundary layer flow over a sphere embedded in a porous medium saturated with a nanofluid. Transp. Porous Media 86, 13–22. [5.6.1]
Chandrasekhara, B. C. and Nagaraju, P. 1993 Composite heat transfer in a variable porosity medium bounded by an infinite flat plate. Wärme-Stoffübertrag. 28, 449–456. [5.1.9.9]
Chandrasekhara, B. C., Radha, N. and Kumari, M. 1992 The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate. Wärme-Stoffübertrag. 27, 157–166. [5.1.9.9]
Chang, I. D. and Cheng, P. 1983 Matched asymptotic expansions for free convection about an impermeable horizontal surface in a porous medium. Int. J. Heat Mass Transfer 26, 163–173. [5.1.6]
Chang, W. J. and Jang, J. Y. 1989a Non-Darcian effects on vortex instability of a horizontal natural convection flow in a porous medium. Int. J. Heat Mass Transfer 32, 529–539. [5.4]
Chang, W. J. and Jang, J. Y. 1989b Inertia effects on vortex instability of a horizontal natural convection flow in a saturated porous medium. Int. J. Heat Mass Transfer 32, 541–550. [5.4]
Chaudary, R. C. and Sharma, P. K. 2003 Three dimensional unsteady convection and mass transfer flow through porous medium. Heat Mass Transfer 39, 765–770. [5.1.9.7]
Chaudhary, M. A., Merkin, J. H. and Pop, I. 1995a Similarity solutions in free-convection boundary-layer flows adjacent to vertical permeable surfaces in porous media. 1. Prescribed surface temperature. Europ. J. Mech. B. 14, 217–237. [5.1.2]
Chaudhary, M. A., Merkin, J. H. and Pop, I. 1996 Natural convection from a horizontal permeable surface in a porous medium—numerical and asymptotic solutions. Transport in Porous Media 22, 327–344. [5.2]
Chaudhary, M. A., Merkin, J. H. and Pop. I. 1995b Similarity solutions in free convection boundary-layer flows adjacent to vertical permeable surfaces in porous media: II prescribed surface heat flux. Heat Mass Transfer 30, 341–347. [5.1.2]
Chaudhary, R. C. and Jain, P. 2010 An exact solution of magnetohydrodynamic convection flow past an accelerated surface embedded in a porous medium. Int. J. Heat Mass Transfer 53, 1609–1611. [5.1.9.9]
Chen, C. H. and Chiou, J. S. 1994 Conjugate free convection heat transfer analysis of a vertical plate fin embedded in non-Darcian porous media. Int. J. Engng Sci. 32, 1703–1716. [5.12.1]
Chen, C. H. and Horng, J. H. 1999 Natural convection from a vertical cylinder in a thermally stratified porous medium. Heat Mass Transfer 34, 423–428. [5.7]
Chen, C. K. and Lin, C. R. 1995 Natural convection from an isothermal vertical surface embedded in a thermally stratified high-porosity medium. Int. J. Engng Sci. 33, 131–138. [5.1.4]
Chen, C. K., Hung, C. I. and Horng, H. C. 1987 Transient natural convection on a vertical flat plate embedded in a high-porosity medium. ASME J. Energy Res. Tech. 109, 112–118. [5.1.3]
Chen, F. and Chen, C. F. 1988 Onset of finger convection in a horizontal porous layer underlying a fluid layer. ASME J. Heat Transfer 110, 403–409. [6.19.1.1, 6.19.1.2, 9.4]
Chen, F. and Chen, C. F. 1996 Analysis of heat transfer regulation and modification using intermittently emplaced porous cavities -- Analysis of flow and heat transfer over an external boundary covered with a porous substrate. ASME J. Heat Transfer 118, 266–267. [5.1.9.5]
Chen, H. T. and Chen, C. K. 1987 Natural convection of non-Newtonian fluids about a horizontal surface in a porous medium. ASME J. Energy Res. Tech. 109, 119–123. [5.2]
Chen, H. T. and Chen, C. K. 1988a Free convection flows of non-Newtonian fluids along a vertical plate embedded in a porous medium. ASME J. Heat Transfer 110, 257–259. [5.1.9.2]
Chen, K. S. and Ho, J. R. 1986 Effects of flow inertia on vertical natural convection in saturated porous media. Int. J. Heat Mass Transfer 29, 753–759. [5.1.7.2]
Cheng, C. Y. 2006b Natural convection heat and mass transfer from a horizontal cylinder of elliptic cross section with constant wall temperature and concentration in saturated porous media. J. Mech. 22, 257–261. [5.5.1]
Cheng, C. Y. 2007b A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model. Int. Comm. Heat Mass Transfer 34, 613–622. [5.5.1s]
Cheng, C. Y. 2012c Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid. Int. Comm. Heat Mass Transfer 39, 931–936. [5.5.1]
Cheng, P. 1977a Constant surface heat flux solutions for porous layer flows. Lett. Heat Mass Transfer 4, 119–128. [5.1.2]
Cheng, P. 1977b The influence of lateral mass flux on free convection boundary layers in a saturated porous medium. Int. J. Heat Mass Transfer 20, 201–206. [5.1.2]
Cheng, P. 1981a Thermal dispersion effects in non-Darcian convective flows in a saturated porous medium. Lett. Heat Mass Transfer 8, 267–270. [5.1.7.3, 5.1.8]
Cheng, P. 1985a Natural convection in a porous medium: external flows. Natural Convection: Fundamentals and Applications (eds. S. Kakaç, W. Aung, and R. Viskanta), Hemisphere, Washington, DC, 475–513. [5, 5.1.7.3, 5.1.8, 5.3, 5.6.1, 5.10.1.2]
Cheng, P. and Ali, C. L. 1981 An experimental investigation of free convection about an inclined surface in a porous medium. ASME 20th National Heat Transfer Conference, Paper No. 81-HT-85. [5.3]
Cheng, P. and Chang, I. D. 1976 On buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces. Int. J. Heat Mass Transfer 19, 1267–1272. [5.2, 6.26]
Cheng, P. and Chang, I. D. 1979 Convection in a porous medium as a singular perturbation problem. Lett. Heat Mass Transfer 6, 253–258. [5.1.6]
Cheng, P. and Chau, W. C. 1977 Similarity solutions for convection of groundwater adjacent to horizontal surface with axisymmetric temperature distribution. Water Resour. Res. 13, 768–772. [5.2]
Cheng, P. and Hsu, C. T. 1984 Higher-order approximations for Darcian free convective flow about a semi-infinite vertical flat plate. ASME J. Heat Transfer 106, 143–151. [5.1.6]
Cheng, P. and Minkowycz, W. J. 1977 Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 82, 2040–2044. [5.1.1, 10.1.5]
Cheng, P. and Pop, I. 1984 Transient free convection about a vertical flat plate imbedded in a porous medium. Int. J. Engng. Sci. 22, 253–264. [5.1.3]
Cheng, P., Ali, C. L. and Verma, A. K. 1981 An experimental study of non-Darcian effects in free convection in a saturated porous medium. Lett. Heat Mass Transfer 8, 261–265. [5.1.8]
Cheng, P., Le, T. T. and Pop, I. 1985 Natural convection of a Darcian fluid about a cone. Int. Comm. Heat Mass Transfer 12, 705–717. [5.8]
Cimpean. D., Merkin, J. H., Pop, I. and Ingham, D. B. 2006 On a free convection problem over a vertical flat surface in a porous medium. Transp. Porous Media 64, 393–411. [5.1.9.9]
Damseh, R. A. and Duwairi, H. M. 2008 Thermophoresis particle deposition: Natural convection interaction from vertical permeable surfaces embedded in a porous medium. J. Porous Media 12, 79–88. [5.1.9.9]
Damseh, R. A., Al-Azab, T. A. and Al-Odat, M. Q. 2008 Unsteady free convection flow of viscoelastic fluid on a stretched vertical plate embedded in a non-Darcian porous medium with constant heat flux. J. Porous Media 11, 117–124. [5.1.9.2]
Daniels, P. G. and Simpkins, P. G. 1984 The flow induced by a heated vertical wall in a porous medium. Q. J. Mech. Appl. Math. 37, 339–354. [5.12.2]
Dash, S., Dash, G. C. and Misra, D. P. 2008 The MHD flow through a porous medium past a stretched vertical permeable surface in the presence of heat source/sink and a chemical reaction. Proc. Nat. Acad. Sci. India A 78, 49–55. [5.1.9.9]
Degan, G. and Vasseur, P. 1995 The non-Darcy regime for boundary layer natural convection from a point source of heat in a porous medium. Int. Comm. Heat Mass Transfer 22, 381–390. [5.11.1]
Degan, G. and Vasseur, P. 2003 Influence of anisotropy on convection in porous media with nonuniform thermal gradient. Int. J. Heat Mass Transfer 46, 781–789. [6.12]
Degan, G., Akowanou, C. and Awanou, N. C. 2007a Transient natural convection of non-Newtonian fluids about a vertical surface embedded in an anisotropic porous medium. Int. J. Heat Mass Transfer 50, 4629–4639. [5.1.9.2]
Degan, G., Vasseur, W. P. and Awanou, N. C. 2005 Anisotropy effects on non-Darcy natural convection from concentrated heat sources in porous media. Acta Mech. 179, 111–124. [5.10.2.2]
Dessaux, A. 1998 Analytical and numerical solutions to a problem of convection in a porous media with lateral mass flux. Int. Comm. Heat Mass Transfer 25, 641–650. [5.1.9.9]
Dutta, P. and Seetharamu, K. N. 1993 Free convection in a saturated porous medium adjacent to a vertical impermeable wall subjected to a non-uniform heat flux. Wärme-Stoffübertrag. 28, 27–32. [5.1.9]
Dwiek, Y. J., Rabadi, N. J. and Ghazzawi, N. A. 1994 Effect of lateral mass flux on free convection from an inclined plate embedded in a saturated porous medium. Arab. J. Sci. Engng. 14, 449–460. [5.3]
Elaiw, A. M. 2008 Vortex instability of mixed convection boundary layer flow adjacent to a non-isothermal inclined surface in a porous medium with variable permeability. ZAMM 88, 121–128. [5.4]
Elaiw, A. M. and Ibrahim, E. S. 2008 Vortex instability of mixed convection boundary layer flow adjacent to a nonisothermal horizontal surface in a porous medium with variable permeability. J. Porous Media 11, 305–321. [5.4]
Elaiw, A. M., Ibrahim, F. S. and Bakr, A. A. 2007 The influence of variable permeability on vortex instability of a horizontal combined free and mixed convection flow in a saturated porous medium. ZAMM 87, 528–536. [5.4]
Elaiw, A. M., Ibrahim, F. S. and Bakr, A. A. 2009 Variable permeability and inertia effect on vortex instability of natural convection flow over horizontal plates in porous media. Comm. Nonlnear Sci. Numer. Simul. 14, 2190–2201. [5.4]
El-Amin, M. F. 2003a Combined effect of magnetic field and viscous dissipation on a power-law fluid over plate with variable surface heat flux embedded in a porous medium. J. Magn. Magn, Mater. 261, 228–237. [5.1.9.2]
El-Amin, M. F. 2004b Non-Darcy free convection from a vertical plate with time-periodic surface oscillations. J. Porous Media 7, 331–338. [5.1.9.7]
El-Amin, M. F. and Ebrahiem, N. A. 2006 Effects of viscous dissipation on unsteady free convection in a fluid past a vertical plate immersed in a porous medium. Transp.Porous Media 64, 1–14. [5.1.9.9]
El-Amin, M. F., El-Hakiem, M. A. and Mansour, M. A. 2003 Effects of viscous dissipation on a power-law fluid over plate embedded in a porous medium. Heat Mass Transfer 39, 807–813. [5.1.9.2]
El-Amin, M. F., El-Hakiem, M. A. and Mansour, M. A. 2004 Combined effect of magnetic field and lateral mass transfer on non-Darcy axisymmetric free convection in a power-law fluid saturated porous medium. J. Porous Media 7, 65–71. [5.2]
El-Amin, M. F., Salama, A. and Abbas, I. 2010 Viscous dissipation effect on natural convection in a fluid saturated porous medium. J. Porous Media 13, 989–997. [5.1.9.4]
El-Amin, M. F., Sun, S., El_Ameen, M. A., Jaha, Y. A. and Gorla, R. S. R. 2011b Non-Darcy free convection of power-law fluids over a two-dimensional body embedded in a porous medium. Transp. Porous Media 86, 965–972. [5.9]
El-Hakiem, M. A. 2001a Thermal dispersion effects on combined convection in non-Newtonian fluids along a non-isothermal vertical plate in a porous medium. Transport in Porous Media 45, 29–40. [8.1.1]
El-Hakiem, M. A. and El-Amin, M. F. 2001a Thermal radiation effect on non-Darcy natural convection with lateral mass transfer. Heat Mass Transfer 37, 161–165. [5.1.9.4]
El-Hakiem, M. A. and El-Amin, M. F. 2001b Mass transfer effects on the non-Newtonian fluids past a vertical plate embedded in a porous medium with non-uniform surface heat flux. Heat Mass Transfer 37, 293–297. [5.1.9.2]
El-Kabeir, S. M. M., El-Hakiem, M. A. and Rashad, A. M. 2008 Group method analysis of combined heat and mass transfer by MHD non-Darcy non-Newtonian natural convection adjacent to horizontal cylinder in a saturated porous medium. Appl. Meth. Mod. 32, 2378–2395.[ [9.2.1]
El-Kabeir, S. M. M., El-Hakiem, M. A. and Rashad, A. M. 2008 Lie group analysis of unsteady MHD three dimensional natural convection from an inclined stretching surface saturated porous medium. J. Comput. Appl. Math. 213, 582–603. [5.3]
Ene, H. I. 1991 Effects of anisotropy on the free convection from a vertical plate embedded in a porous medium. Transport in Porous Media 6, 183–194. [5.1.9.5]
Ene, H. I. and Polievski, D. 1987 Thermal Flow in Porous Media, Reidel, Dordrecht. [1.4.3, 5.6.2, 5.11.2]
Ettefagh, J., Vafai, K. and Kim, S. J. 1991 Non-Darcian effects in open ended cavities filled with a porous medium. ASME J. Heat Transfer 113, 747–756. [5.12.3]
Evans, G. H. and Plumb, O. A. 1978 Natural convection from a vertical isothermal surface imbedded in a saturated porous medium. AIAA-ASME Thermophysics and Heat Transfer Conf., Paper 78-HT −55, Palo Alto, California. [5.1.7.1, 5.1.8]
Fand, R. M. and Yamamoto, L. H. 1990 Heat transfer by natural convection from a horizontal cylinder embedded in a porous medium: the wall effect. Heat Transfer 1990, Hemisphere, New York, 5, 183–188. [5.5.2]
Fand, R. M., Steinberger, T. E. and Cheng, P. 1986 Natural convection heat transfer from a horizontal cylinder embedded in a porous medium. Int. J. Heat Mass Transfer 29, 119–133. [5.5.2]
Fand, R. M., Varahasamy, M. and Yamamoto, L. M. 1994 Heat transfer by natural convection from horizontal cylinders embedded in porous media whose matrices are composed of spheres: viscous dissipation. Heat Transfer 1994, Inst. Chem. Engrs., Rugby, vol. 5, pp. 237–242. [5.5.1]
Ferdows, M., Kaino, K. and Sivasankaran, S. 2009 Free convection flow in an inclined porous surface. J. Porous Media 12, 997–1003. [5.3]
Ganapathy, R. 1992 Thermal convection in an infinite porous medium due to a source in a sphere. Fluid Dyn. Res. 9, 223–234. [5.11.2]
Ganapathy, R. 1997 Thermal convection in an infinite porous medium induced by a heated sphere. ASME J. Heat Transfer 119, 647–650. [5.6.2]
Ganapathy, R. and Purushothaman, R. 1990 Thermal convection from an instantaneous point heat source in a porous medium. Int. J. Engng. Sci. 28, 907–918. [5.11.2]
Gill, U. S. and Minkowycz, W. J. 1988 Boundary and inertia effects on conjugate mixed convection heat transfer from a vertical plate fin in a high-porosity porous medium. Int. J. Heat Mass Transfer 31, 419–427. [5.12.1]
Gorla, R. S. R. and Bakier, A. Y. 2011 Thermal analysis of natural convection and radiation in porous fins. Int. Comm. Heat Mass Transfer 38, 638–645. [5.12.1]
Gorla, R. S. R. and Chamkha, A. 2011 Natural convective boundary layer flow over a non-isothermal vertical plate embedded in a porous medium saturated with a nanofluid. Nanoscale Microscale Thermophys. Engng. 15, 81–94. [5.1.9.9]
Gorla, R. S. R. and Kumari, M. 2003 Free convection in non-Newtonian fluids along a horizontal plate in a porous medium. Heat Mass Transfer 39, 101–106. [5.2]
Gorla, R. S. R. and Tornabene, R. 1988 Free convection from a vertical plate with nonuniform surface heat flux and embedded in a porous medium. Transport in Porous Media 3, 95–105. [5.1.9.9]
Gorla, R. S. R. and Zinalabedini, A. H. 1987 Free convection from a vertical plate with nonuniform surface temperature and embedded in a porous medium. ASME J. Energy Res. Tech. 109, 27–30. [5.1.9.9]
Gorla, R. S. R., Mansour, M. A., Hasssanien, I. A. and Bakier, A. Y. 1999a Mixed convection effect on melting from a vertical plate in a porous medium. Transport Porous Media 36, 245–254. [10.1.7]
Guria, M., Manna, G. and Jana, R. N. 2010 Flow and heat transfer along an infinite horizontal porous plate through a porous medium in a rotating system. J. Porous Media 13, 387–393. [5.2]
Haddad O.M., Al-Nimr, M. A. and Al-Khateeb, A. N. 2004 Validation of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium. Int. J. Heat Mass Transfer 47, 2037–2042. [5.1.9.3]
Haddad O.M., Al-Nimr, M. A. and Al-Khateeb, A. N. 2005 Validity of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium. J. Porous Media 8, 85–95. [5.1.9.3]
Haddad, O. M., Abuzaid, M. M. and Al-Nimr, M. A. 2005 Developing free-convection gas flow in a vertical open-ended microchannel filled with porous media. Numer. Heat Transfer A 48, 693–710. [7.1.7]
Hady, F. M., Ibrahim, F. S., Abdel-Gaied, S. M. and Eid, M. R. 2011 Influence of yield stress on free convective boundary layer flow of a non-Newtonian nanofluid past a vertical plate in a porous medium. J. Mech. Sci. Tech. 25, 2043–2050. {5.9.2]
Hamad, M. A. A. and Pop, I. 2011 Scaling transformations for boundary layer flow near the stagnation point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects. Transp. Porous Media 87, 25–39. [5.1.9.9]
Haq, S. and Mulligan, J. C. 1990a Transient free convection about a vertical flat plate embedded in a saturated porous medium. Numer. Heat Transfer A 18, 227–242. [5.1.3]
Haq, S. and Mulligan, J. C. 1990b Transient free convection from a vertical plate to a non-Newtonian fluid in a porous medium. J. Non-Newtonian Fluid Mech. 36, 395–440. [5.1.9.2]
Harris, S. D. and Ingham, D. B. 2004 Techniques for solving the boundary-layer equations. In Emerging Technologies and Techniques in Porous Media (D. B. Ingham, A. Bejan, E. Mamut and I. Pop, eds), Kluwer Academic, Dordrecht, pp. 43–64. [5.1.3]
Harris, S. D., Ingham, D. B. and Pop, I. 1996 Transient free convection from a vertical plate subjected to a change in surface heat flux in porous media. Fluid Dyn. Res. 18, 313–324. [5.1.3]
Harris, S. D., Ingham, D. B. and Pop, I. 1997a Free convection from a vertical plate in a porous media subjected to a sudden change in surface temperature. Int. Comm. Heat Mass Transfer 24, 543–552. [5.1.3]
Harris, S. D., Ingham, D. B. and Pop, I. 1997b Free convection from a vertical plate in a porous medium subjected to a sudden change in surface heat flux. Transport in Porous Media 26, 205–224. [5.1.3]
Harris, S. D., Ingham, D. B. and Pop, I. 2000 Transient free convection from a horizontal surface in a porous medium subjected to a sudden change in surface heat flux. Transport Porous Media 39, 97–117. [5.2]
Hassanien, I. A. and Eliaw, A. M. 2007 Variable permeability effect on buoyancy-induced inclined boundary layer flow in a saturated porous medium with variable wall temperature. Heat Mass Transfer 43, 1241–1247. [5.3]
Hassanien, I. A., Essawy, A. H. and Moursy, N. M. 2003b Variable viscosity and thermal conductivity effects on heat transfer by natural convection from a cone and a wedge in porous media. Arch. Mech. 55, 345–356. [5.8]
Hassanien, I. A., Essawy, A. H. and Moursy, N. M. 2004 Natural convection flow of micropolar fluid from a permeable uniform heat flux surface in porous medium. Appl. Math. Comput. 152, 3232–335. [5.1.9.2]
Hassanien, I. A., Ibrahim, F. S. and Omer, G. M. 2006 Unsteady flow and heat transfer of a viscous fluid in the stagnation region of a three-dimensional body embedded in a porous medium. J. Porous Media 9, 357–372. [5.9]
Hassanien, I. A., Ibrahim, F. S. and Omer, G.M. 2005 The effect of variable permeability and viscous dissipation on a non-Darcy natural-convection regime with thermal dispersion. J. Porous Media 8, 237–256. [5.1.9.4]
Hassanien, I. A., Salama, A. A. and Elaiw, A. M. 2004a The onset of longitudinal vortices in mixed convection flow over an inclined surface in a porous medium with variable permeability. Appl. Math. Comput. 154, 313–333. [8.1.2]
Hassanien, I. A., Salama, A. A. and Elaiw, A. M. 2004b Variable permeability effect on vortex instability of a horizontal natural convection flow in a saturated porous medium with a variable wall temperature. Zeit. Angew. Math. Mech. 84, 39–47. [5.4]
Hassanien, I. A., Salama, A. A. and Moursy, N. M. 2004c Non-Darcian effects on vortex instability of mixed convection over horizontal plates porous medium with surface mass flux. Int. Comm. Heat Mass Transfer 31, 231–240. [8.1.2]
Hassanien, I. A., Salama, A. A. and Moursy, N. M. 2004d Inertia effect on vortex instability of horizontal natural convection flow in a saturated porous medium with surface mass flux. Int. Comm. Heat Mass Transfer 31, 741–750. [5.4]
Hayat, T., Abbas, Z. and Asghar, S. 2007a Effects of Hall current and heat transfer on the flow in a porous medium with slip condition. J. Porous Media 10, 35–50. [5.1.9.9]
Hayat, T., Hussain, M., Nadeem, S. and Mesioub, S. 2011 Falkner-Skan wedge flow of a power-law fluid with mixed convection and porous medium. Compt. Fluids 49, 22–28. [8.4.3]
Hayat, T., Mustafa, M., Pop, I. and Obaidat, S. 2011 Flow and heat transfer due to stretching surface in an anisotropic porous medium filled with a viscoelastic fluid J. Porous Media 14, 523–532. [5.1.9.9]
Hayat, T., Sajjad, R., Abbas, Z., Sajid, M. and Hendi, A. A. 2011 Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium. Int. J. Heat Mass Transfer 54, 854–862. [7.1.6]
Helmy, K. A. 1998 MHD unsteady free convection flow past a vertical porous plate. Z. Angew. Math. Mech. 78, 255–270. [5.1.9.9]
Herwig, H. and Koch, M. 1990 An asymptotic approach to natural convection momentum and heat transfer in saturated highly porous media. ASME J. Heat Transfer 112, 1085–1088. [5.1.9.9, 9.7]
Hickox, C. E. 1981 Thermal convection at low Rayleigh number from concentrated sources in porous media. ASME J. Heat Transfer 103, 232–236. [5.11.2]
Hickox, C. E. and Watts, H. A. 1980 Steady thermal convection from a concentrated source in a porous medium. ASME J. Heat Transfer 102, 248–253. [5.11.3]
Higuera, F. J. 1997 Conjugate natural convection heat transfer between two porous media separated by a horizontal wall. Int. J. Heat Mass Transfer 40, 3157–3161. [5.1.5]
Higuera, F. J. and Pop, I. 1997 Conjugate natural convection heat transfer between two porous media separated by a vertical wall. Int. J. Heat Mass Transfer, 40, 123–129. [5.1.5]
Higuera, F. J. and Weidman, P. D. 1995 Natural convection beneath a downward facing heated plate in a porous medium. Eur. J. Mech. B/Fluids 14, 29–40. [5.2]
Higuera, F. J. and Weidman, P. D. 1998 Natural convection far downstream of a heat source on a solid wall. J. Fluid Mech. 361, 225–39. [5.11.1]
Hong, J. T. and Tien, C. L. 1987 Analysis of thermal dispersion effect on vertical-plate natural convection in porous media. Int. J. Heat Mass Transfer 30, 143–150. [5.1.7.3]
Hong, J. T., Tien, C. L. and Kaviany, M. 1985 Non-Darcian effects on vertical-plate natural convection in porous media with high porosities. Int. J. Heat Mass Transfer 28, 2149–2157. [5.1.7.2]
Hong, J. T., Yamada, Y. and Tien, C. L. 1987 Effects of non-Darcian and nonuniform porosity on vertical-plate natural convection in porous media. ASME J. Heat Transfer 109, 356–362. [5.1.7.1, 5.1.7.2]
Hossain, M. A. and Nakayama, A. 1993 Non-Darcy free convective flow along a vertical cylinder embedded in a porous medium with surface mass flux. Int. J. Heat Fluid Flow 14, 385–390. [4.3]
Hossain, M. A. and Nakayama, A. 1994 Nonsimilar free convection boundary layer in non-Newtonian fluid saturated porous media. AIAA J. Thermophys. Heat Transfer 8, 107–112. [5.1.9.2]
Hossain, M. A. and Pop, I. 1997 Radiation effect on Darcy free convection flow along an inclined surface placed in porous media. Heat Mass Transfer 32, 223–227. [5.3]
Hossain, M. A. and Pop, I. 2001 Radiation effects on free convection over a vertical flat plate embedded in a porous medium with high porosity. Int. J. Therm. Sci. 40, 289–295. [5.1.9.4]
Hossain, M. A. and Rees, D. A. S. 1997 Non-Darcy free convection along a horizontal heated surface. Transport Porous Media 29, 309–321. [5.2]
Hossain, M. A., Pop, I. and Rees, D. A. S. 2000 The effect of time-periodic surface oscillations on free convection from a vertical surface in a porous medium. Transport Porous Media 39, 119–130. [5.1.9.7]
Hossain, M.A., Nakayama, A. and Pop, I. 1995 Conjugate free convection of non-Newtonian fluids about a vertical cylindrical fin in porous media. Heat Mass Transfer 30, 149–153. [5.12.1]
Hsu, C. T. and Cheng, P. 1979 Vortex instability in buoyancy-induced flow over inclined heated surfaces in porous media. ASME J. Heat Transfer 101, 660–665. [5.4]
Hsu, C. T. and Cheng, P. 1985a Effects of upstream geometry on natural convection of a Darcian fluid about a semi-infinite inclined heated surface. ASME J. Heat Transfer 107, 283–292. [5.12.2]
Hsu, C. T. and Cheng, P. 1985b The Brinkman model for natural convection about a semi-infinite vertical flat plate in a porous medium. Int. J. Heat Mass Transfer 28, 683–697. [5.1.7.1]
Hsu, C. T., Cheng, P. and Homsy, G. M. 1978 Instability of free convective flow over a horizontal impermeable surface in a porous medium. Int. J. Heat Mass Transfer 21, 1221–1228. [5.4]
Huang, M. J. and Chen, C. K. 1985 Effects of surface mass transfer on free convection flow over vertical cylinder imbedded in a saturated porous medium. ASME J. Energy Resources Tech. 107, 394–396. [5.7]
Huenefeld, J. S. and Plumb, O. A. 1981 A study of non-Darcy natural convection from a vertical heated surface in a saturated porous medium. ASME 20th National Heat Transfer Conf. Paper 81-HT-45. [5.1.8]
Hung, C. I. 1991 Note on conjugate natural convection-conduction heat transfer for a vertical plate fin embedded in high-porosity medium. Int. J. Non-linear Mech. 26, 135–140. [5.12.1]
Hung, C. I. and Chen, C. B. 1997 Non-Darcy free convection in a thermally stratified porous medium along a vertical plate with variable heat flow. Heat Mass Transfer 33, 101–107. [5.1.4]
Hung, C. I., Chen, C. H. and Chen, C. B. 1999 Non-Darcy free convection along a nonisothermal vertical surface in a thermally stratified porous medium. Int. J. Engng. Sci. 37, 477–495. [5.1.4]
Hung, C. I., Chen, C. K. and Cheng, P. 1989 Transient conjugate natural convection heat transfer along a vertical plate fin in a high-porosity medium. Numer. Heat Transfer 15, 133–148. [5.12.1]
Husnain, S., Mehmood, A., Beg, O. A. and Ali, A. 2012 Suction and blowing effects on unsteady flow and heat transfer through porous media with variable viscosity. J. Porous Media 15, 293–302. [5.1.9.9]
Imadojemu, H. and Johnson, R. 1991 Convective heat transfer from a heated vertical plate surrounded by a saturated porous medium. Proc. ASME & JSME Thermal Engineering Joint Conference—1991. vol.4, pp. 203–212. [5.1.8]
Ingham D. B., Merkin, J. H. and Pop, I. 1985a Flow past a suddenly cooled horizontal flat surface in a saturated porous medium. Acta Mech. 57, 183–202. [5.3]
Ingham, D. B. 1986 The non-Darcy free convection boundary layer on axi-symmetric and two-dimensional bodies of arbitrary shape. Int. J. Heat Mass Transfer 29, 1759–1760. [5.9]
Ingham, D. B. 1988 An exact solution for non-Darcy free convection from a horizontal line source. Wärme-Stoffübertrag. 22, 125–127. [5.10.1.1, 5.10.1.2]
Ingham, D. B. and Brown, S. N. 1986 Flow past a suddenly heated vertical plate in a porous medium. Proc. Roy. Soc. London Ser. A 403, 51–80. [5.1.3]
Ingham, D. B. and Pop, I. 1987a Darcian free convective flow about an impermeable horizontal surface bounded by a vertical wall. Int. J. Engng. Sci. 25, 373–383. [5.12.2]
Ingham, D. B. and Pop, I. 1987b Free convection from a semi-infinite vertical surface bounded by a horizontal wall in a porous medium. Int. J. Heat Mass Transfer 30, 1615–1622. [5.12.2]
Ingham, D. B. and Pop, I. 1987c Natural convection about a heated horizontal cylinder in a porous medium. J. Fluid Mech. 184, 157–181. [5.5.2]
Ingham, D. B. and Pop, I. 1988 Higher-order effects in natural convection flow over uniform flux inclined flat plates in porous media. Wärme-Stoffübertrag. 22, 239–242. [5.3]
Ingham, D. B., Merkin, J. H. and Pop, I. 1982 Flow past a suddenly cooled vertical flat surface in a saturated porous medium. Int. J. Heat Mass Transfer 25, 1916–1919. [5.1.3]
Ingham, D. B., Merkin, J. H. and Pop, I. 1985b Natural convection from a semi-infinite flat plate inclined at a small angle to the horizontal in a saturated porous medium. Acta Mech. 57, 183–202. [5.3]
Israel-Cookey, C., Ogulu, A. and Omubo-Pepple, Ichimiya, K. 2003 Influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with time-dependent suction. Int. J. Heat Mass Transfer 46, 2305–2311. [5.1.9.4]
Jaiswal, B. S. and Soundalgekar, V. M. 2001 Oscillating plate temperature effects on a flow past an infinite vertical porous plate with constant suction and embedded in a porous medium. Heat Mass Transfer 37, 125–131. [5.1.9.7]
Jamin, Y. L. and Mohamad, A. A. 2008 Natural convection heat transfer enhancements from a cylinder using porous carbon foam: Experimental study. ASME J. Heat Transfer 130, #122502. [5.5.1]
Jang, J. Y. and Chang, W. J. 1987 Vortex instability of inclined buoyant layer in porous media saturated with cold water. Int. Comm. Heat Mass Transfer 14, 405–416. [5.4]
Jang, J. Y. and Chang, W. J. 1988a Vortex instability of buoyancy-induced inclined boundary layer flow in a saturated porous medium. Int. J. Heat Mass Transfer 31, 759–767. [5.4]
Jang, J. Y. and Chang, W. J. 1988d Buoyancy-induced inclined boundary layer flow in a saturated porous medium. Comput. Methods Appl. Mech. 68, 333–344. [5.3]
Jang, J. Y. and Chang, W. J. 1989 Maximum density effects on vortex instability of horizontal and inclined buoyancy-induced flows in porous media. ASME J. Heat Transfer 111, 572–574. [5.3]
Jang, J. Y. and Chen, J. L. 1993a Thermal dispersion and inertia effects on vortex instability of a horizontal mixed convection flow in a saturated porous medium. Int. J. Heat Mass Transfer 36, 383–389. [5.4]
Jang, J. Y. and Chen, J. L. 1993b Variable porosity effect on vortex instability of a horizontal mixed convection flow in a saturated porous medium. Int. J. Heat Mass Transfer 36, 1573–1583. [5.4]
Jang, J. Y. and Chen, J. L. 1994 Variable porosity and thermal dispersion effects on vortex instability of a horizontal natural convection flow in a saturated porous medium. Wärme-Stoffübertrag. 29, 153–160. [5.4]
Jang, J. Y. and Hsu, C. T. 2007 Effects of magnetohydrodynamics on the vortex instability of natural convection flow over a horizontal plate in a saturated porous medium. J. Chinese Soc. Mech. Engrs. 28, 71–80. [5.4]
Jang, J. Y. and Hsu, C. T. 2009b Vortex instability of MHD natural convection flow over a horizontal plate in a porous medium. Comput. Fluids 38, 333–339. [5.4]
Jang, J. Y. and Leu, J. S. 1992 Buoyancy-induced boundary layer flow of liquid in a porous medium with temperature-dependent viscosity. Int. Comm. Heat Mass Transfer 19, 435–444. [5.1.9.9]
Jang, J. Y. and Leu, J. S. 1993 Variable viscosity effects on the vortex instability of free convection boundary layer flow over a horizontal surface in a porous medium. Int. J. Heat Mass Transfer 36, 1287–1294. [5.4]
Jang, J. Y. and Lie, K. N. 1992 Vortex instability of mixed convection flow over horizontal and inclined surfaces in a porous medium. Int. J. Heat Mass Transfer 35, 2077–2085. [5.4]
Johnson, C. H. and Cheng, P. 1978 Possible similarity solutions for free convection boundary layers adjacent to flat plates in porous media. Int. J. Heat Mass Transfer 21, 709–718. [5.1.9.9]
Joshi, V. and Gebhart, B. 1984 Vertical natural convection flows in porous media: calculations of improved accuracy. Int. J. Heat Mass Transfer 27, 69–75. [5.1.6]
Kaviany, M. and Mittal, M. 1987 Natural convection heat transfer from a vertical plate to high permeability porous media: an experiment and an approximate solution. Int. J. Heat Mass Transfer 30, 967–978. [5.1.7.2, 5.1.8]
Kayhani, M. H., Khaje, E. and Sadi, M. 2011 Natural convection boundary layer along impermeable inclined surfaces embedded in porous medium. Mechanika (1) 64–70. [5.3]
Kayhani, M. H., Nazari, M. and Shakeri, E. 2011 Effects of fluid-to-solid conductivity ratio, Rayleigh number and interstitial heat transfer coefficient on TNE free convection in a porous enclosure. Transp. Porous Media 87, 625–633. [7.6.2]
Kechil, S. A. and Hashim, I. 2008 Series solutions of boundary-layer flows in porous media with lateral mass flux. Heat Mass Transfer 44, 1179–1186. [5.1.2]
Khadrawi, A. F. and Al-Nimr, M. A. 2005 The effect of the local inertial term on the transient free convection from a vertical plate inserted in a semi-infinite domain partly filled with porous material. Transport Porous Media 59, 139–153. [5.1.3]
Khan, I., Fakhar, K. and Shafie, S. 2011 Magnetohydrodynamic free convection flow past an oscillating plate embedded in a porous medium. J. Phys. Soc. Japan 80, #104401. [5.1.9.9]
Khani, F., Farmany, A., Raji, M. A., Aziz, A. and Samadi, F. 2009 Analytic solution for heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects. Comm. Nonlinear Sci. Numer. Simul. 14, 3867–3878. [5.1.9.9]
Kim, K. H., Kim, S. J. and Hyun, J. M. 2004 Development of boundary layers in transient convection about a vertical plate in a porous medium. J. Porous Media 7, 249–259. [5.1.3]
Kim, M. C., Kim, K.Y. and Kim, S. 2004 The onset of transient convection in fluid-saturated porous layer. Int. Comm. Heat Mass Transfer 31, 53–62. [6.11.3]
Kim, S. J. and Vafai, K. 1989 Analysis of natural convection about a vertical plate embedded in a porous medium. Int. J. Heat Mass Transfer 32, 665–677. [5.1.7.1]
Kim, Y. J. 2001a Unsteady MHD convection flow of polar fluids past a vertical moving porous plate in a porous medium. Int. J. Heat Mass Transfer 44, 2791–2799. [5.1.9.2]
Kim, Y. J. 2001b Unsteady convection flow of micropolar fluids past a vertical porous plate embedded in a porous medium. Acta Mech. 148, 105–116. [5.1.9.2]
Kimura, S. 1989b Transient forced and natural convection heat transfer about a vertical cylinder in a porous medium. Int. J. Heat Mass Transfer 32, 617–620. [4.6.4, 5.7]
Kimura, S. and Bejan, A. 1985 Natural convection in a stably heated corner filled with porous medium. ASME J. Heat Transfer 107, 293–298. [5.12.2]
Kimura, S. and Pop, I. 1992b Conjugate free convection from a circular cylinder in a porous medium. Int. J. Heat Mass Transfer 35, 3105–3113. [5.5.1]
Kimura, S. and Pop, I. 1994 Conjugate free convection from a sphere in a porous medium. Int. J. Heat Mass Transfer 37, 2187–2192. [5.6.1]
Kimura, S., Bejan, A., and Pop, I. 1985 Natural convection near a cold plate facing upward in a porous medium. ASME J. Heat Transfer 107, 819–825. [5.2]
Kimura, S., Kiwata, T., Okajima, A. and Pop, I. 1997 Conjugate natural convection in porous media. Adv. Water Resource, 20, 111–126. [5.12.3]
Kiwan, S. 2007a Effect of radiative losses on the heat transfer from porous fins. Int. J. Therm. Sci. 46, 1046–1055. [5.12.1]
Kiwan, S. 2007b Thermal analysis of natural convection porous fins. Transp. Porous Media 67, 17–29. [5.12.1]
Kiwan, S. and Ali, M. E. 2008 Near-slit effects on the flow and heat transfer from a stretching plate in a porous medium. Numer. Heat TransferA 54, 93–108. [5.1.9.9]
Kokubun, M. A. E. and Fachini, F. F. 2011 An analytical approach to Hiemenz flow in a porous medium with heat exchange. Int. J. Heat Mass Transfer 54, 3613–3621. [5.1.9.3]
Kou H. S. and Huang, D. K. 1996a Some transformations for natural convection on a vertical flat plate embedded in porous media with prescribed wall temperature. Int. Comm. Heat Transfer 23, 273–286. [5.1.9.9]
Kou, H. S. and Huang, D. K. 1996b Possible transformations for natural convection on a vertical flat plate embedded in porous media with prescribed wall heat flux. Int. Comm. Heat Transfer 23, 1031–1042. [5.1.9.9]
Kumaran, V. and Pop, I. 2006 Steady free convective boundary layer over a flat plate embedded in a porous medium filled with water at 4°C. Int. J. Heat Mass Transfer 49, 3240–3252. [5.1.9.9]
Kumari, M. 2001a Effect of variable viscosity on non-Darcy free or mixed convection flow on the horizontal surface in a saturated porous medium. Int. Comm. Heat Mass Transfer 28, 723–732. [5.2, 8.1.2]
Kumari, M. 2001b Variable viscosity effects on free and mixed convection boundary layer flow from a horizontal surface in a saturated porous medium – variable heat flux. Mech. Res. Commun. 28, 339–348. [5.2]
Kumari, M. and Jayanthi, S. 2004 Non-Darcy non-Newtonian free convection flow over a horizontal cylinder in a saturated porous medium. Int. Comm. Heat Mass Transfer 31, 1219–1226. [5.5.1]
Kumari, M. and Jayanthi, S. 2005 Uniform lateral mass flux on natural-convection flow over a vertical cone embedded in a porous medium saturated with a non-Newtonian fluid. J. Porous Media 8, 73–84. [5.8]
Kumari, M. and Nath, G. 2009c Unsteady natural convection flow over a heated cylinder buried in a fluid-saturated porous medium. J. Porous Media 12, 1225–1235. [5.5.1]
Kumari, M. and Nath, G. 2010 Natural convection on a horizontal cone in a porous medium with non-uniform wall temperature/concentration or heat/mass flux and suction/injection. Transp. Porous Media 84, 275–284. [5.8]
Kumari, M., Pop, I. and Nath, G. 1985 Non-Darcy natural convection from a heated vertical plate in saturated porous media with mass transfer. Int. Comm. Heat Mass Transfer 12, 337–346. [5.1.7.2]
Kurdyumov, V. N. and Liñán, A. 2001 Free and forced convection around line sources of heat and heated cylinders in porous media. J. Fluid Mech. 427, 389–409. [5.5.1]
Lage, J. L. and Bejan, A. 1991 Natural convection from a vertical surface covered with hair. Int. J. Heat Fluid Flow 12, 46–53. [5.13]
Lai, F. C. 1991b Non-Darcy natural convection from a line source of heat in a saturated porous medium. Int. Comm. Heat Mass Transfer 18, 445–457. [5.10.1.2]
Lai, F. C., Pop, I and Kulacki, F. A. 1991b Natural convection from isothermal plates embedded in thermally stratified porous media. AIAA J. Thermophys. Heat Transfer 4, 533–535. [5.1.4]
Lai, F. C., Pop, I. and Kulacki, F. A. 1990c Free and mixed convection from slender bodies of revolution in porous media. Int. J. Heat Mass Transfer 33, 1767–1769. [5.9, 8.1.4]
Lai, F.C. 1990b Natural convection from a concentrated heat source in a saturated porous medium. Int. Comm. Heat Mass Transfer 17, 791–800. [5.11.1]
Lee, D. H., Yoon, D. Y. and Choi, C. K. 2000 The onset of vortex instability in laminar convection flow over an inclined plate embedded in a porous medium. Int. J. Heat Mass Transfer 43, 2895–2908. [5.4]
Lee, H. M. 1983 An experimental study of natural convection about an isothermal downward-facing inclined surface in a porous medium. M.S. Thesis, University of Hawaii. [5.3]
Lesnic, D. and Pop, I. 1998a Free convection in a porous medium adjacent to horizontal surfaces. Zeit. Angew. Math. Mech. 78, 197–205. [5.2]
Lesnic, D., Ingham, D. B. and Pop, I. 1995 Conjugate free convection from a horizontal surface in a porous medium. Z. Angew. Math. Mech. 75, 715–722. [5.2]
Lesnic, D., Ingham, D. B. and Pop, I. 1999 Free convection boundary-layer flow along a vertical surface in a porous medium with Newtonian heating. Int. J. Heat Mass Transfer 42, 2621–2627. [5.1.9.8]
Lesnic, D., Ingham, D. B. and Pop, I. 2000 Free convection from a horizontal surface in a porous medium with Newtonian heating. J. Porous Media 3, 227–235. [5.2]
Lesnic, D., Ingham, D. B., Pop, I. and Storr, C. 2004 Free convection boundary-layer flow above a nearly horizontal surface in a porous medium with Newtonian heating. Heat Mass Transfer 40, 665–672. [5.3]
Leu, J. S. and Jang, J. Y. 1994 The wall and free plumes above a horizontal line source in non-Darcian porous media. Int. J. Heat Mass Transfer 37, 1925–1933. [5.10.1]
Leu, J. S. and Jang, J. Y. 1993 Variable viscosity effects on the vortex instability of the convective boundary layer flow over a horizontal uniform heat flux surface in a saturated porous medium. Proc. 6th Int. Sympos. Transport Phenomena and Thermal Engineering, Seoul, Korea. Vol.1, pp. 203–208. [5.4]
Leu, J. S. and Jang, J. Y. 1995 The natural convection from a point heat source embedded in a non-Darcian porous medium. Int. J. Heat Mass Transfer 38, 1097–1104. [5.11.1]
Lewis, S., Bassom, A. P. and Rees, D. A. S. 1995 The stability of vertical thermal boundary-layer flow in a porous medium. Eur. J. Mech. B/Fluids 14, 395–407. [5.1.9.9]
Liao, S. J. and Magyari, E. 2006 Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Z. Angew. Math. Phys. 57, 777–792. [5.1.9.9]
Liao, S. J. and Pop, I. 2004 Explicit analytic solution for similarity boundary layer equations. Int. J. Heat Mass Transfer 47, 75–85. [5.1.9.1]
Libera, J. and Poulikakos, D. 1990 Parallel-flow and counter-flow conjugate convection from a vertical insulated pipe. AIAA J. Thermophys. Heat Transfer 4, 400–404. [5.7]
Lie, K. N. and Jang, J. Y. 1993 Boundary and inertia effects on vortex instability of a horizontal mixed convection flow in a porous medium. Numer. Heat Transfer A 23, 361–378. [5.4]
Lin, D. S. and Gebhart, B. 1986 Buoyancy induced flow adjacent to a horizontal surface submerged in porous medium saturated with cold water. Int. J. Heat Mass Transfer 29, 611–623. [5.2]
Liu, C. Y. and Guerra, A. C. 1985 Free convection in a porous medium near the corner of arbitrary angle formed by two vertical plates. Int. Comm. Heat Mass Transfer 12, 431–440. [5.12.2]
Liu, C. Y. and Ismail, K. A. R. 1980 Asymptotic solution of free convection near a corner of two vertical porous plates embedded in a porous medium. Lett. Heat Mass Transfer 7, 457–463. [5.12.2]
Liu, C. Y., Lam, C. Y. and Guerra, A. C. 1987a Free convection near a corner formed by two vertical plates embedded in a porous medium. Int. Comm. Heat Mass Transfer 14, 125–136. [5.12.2]
Liu, I. C. 2006 Flow and heat transfer of viscous fluids saturated in porous media over a permeable non-isothermal stretching sheet. Transport Porous Media 64, 375–392. [5.1.9.9]
Liu, J. Y. and Minkowycz, W. J. 1986 The effect of Prandtl number on conjugate heat transfer in porous media. Int. Comm. Heat Mass Transfer 13, 439–448. [5.12.1]
Liu, J. Y., Shih, S. D. and Minkowycz, W. J. 1987b Conjugate natural convection about a vertical cylindrical fin with lateral mass flux in a saturated porous medium. Int. J. Heat Mass Transfer 30, 623–630. [5.12.1]
Magyari, E. 2006 Paradox of the Darcy free convection over vertical plate with prescribed inverse linear surface heat flux. J. Porous Media 9, 663–670. [5.1.9.8s]
Magyari, E. 2011b Comment on “A novel analytical solution of mixed convection about an inclined flat plate embedded in a porous medium using the DTM-Pade” by M. M. Rashidi, N. Laraqi and S. M. Sadri, Int. J. Thermal Sciences 49 (2010) 2406–2412. Int. J. Therm. Sci. 50, 1339–1342. [8.1.1]
Magyari, E. 2010a onsequences of the transition invariance on the Darcy free convection flow past a vertical surface. Transp. Porous Media 85, 757–769. [5.1.9.9]
Magyari, E. 2011c Reply on the reply on the Note : “Scaling transformations for boundary layer flow near the stagnation point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects.” Transp. Porous Media 87, 53–56. [5.1.9.9]
Magyari, E. and Keller, B. 2000 Exact analytic solutions for free convection boundary layers on a heated vertical plate with lateral mass flux embedded in a saturated porous medium. Heat Mass Transfer 36, 109–116. [5.1.9.1]
Magyari, E. and Keller, B. 2003a The opposing effect of viscous dissipation allows for a parallel free convection boundary-layer flow along a cold vertical flat plate. Transport Porous Media 51, 227–230. [5.1.9.4]
Magyari, E. and Keller, B. 2003b Effect of viscous dissipation on a quasi-parallel free convection boundary-layer flow over a vertical plate in a porous medium. Transport Porous Media 51, 231–236. [5.1.9.4]
Magyari, E. and Keller, B. 2003c Buoyancy sustained by viscous dissipation. Transport Porous Media 53, 105–115. [5.9.4]
Magyari, E. and Keller, B. 2004a The free convection boundary-layer flow induced in a fluid-saturated porous medium by a non-isothermal vertical cylinder approaches the shape of Schlicting’s round jet as the porous radius tends to zero. Transport Porous Media 54, 265–271. [5.7]
Magyari, E. and Keller, B. 2004b Backward free convection boundary layers in porous media. Transport Porous Media 55, 285–300. [5.1.9.1]
Magyari, E. and Rees, D. A. S. 2005 Effect of viscous dissipation on the Darcy free convection boundary-layer flow over a vertical plate with exponential temperature distribution in a porous medium. Fluid Dyn. Res. (submitted). [5.1.9.4]
Magyari, E. and Rees, D. A. S. 2006 Effect of viscous dissipation on the Darcy free convection boundary-layer flow over a vertical plate with exponential distribution in a porous medium. Fluid Dyn. Res. 38, 405–429. [5.1.9.4]
Magyari, E., Pop, I. and Keller, B. 2003c New analytic solutions of a well-known boundary value problem in fluid mechanics. Fluid Dyn. Res. 33, 313–317. [5.1.9.1]
Magyari, E., Pop, I. and Keller, B. 2004 Analytical solutions for unsteady free convection in porous media. J. Engng. Math. 48, 93–104. [5.1.9.1]
Magyari, E., Rees, D. A. S. and Keller, B. 2005b Effect of viscous dissipation on the flow in fluid saturated porous media. Handbook of Porous Media (ed. K. Vafai), 2nd ed., Taylor and Francis, New York, pp. 373–406. [2.2.2, 5.1.9.4, 6.6]
Mahdy, A. 2009 MHD non-Darcian free convection from a vertical wavy surface embedded in porous media. Int. Comm. Heat Mass Transfer 36, 1067–1074 [5.1.9.9]
Mahdy, A., Mohamed, R. A. and Hady, F. M. 2008 The influence of magnetic field on natural convection flow near a wavy cone in porous media. Latin Amer. Appl. Res. 38, 155–160. [5.8]
Mahmood, T. and Merkin, J. H. 1998 The convective boundary-layer flow on a reacting surface in a porous medium. Transport Porous Media 32, 285–298. [3.4, 5.12.3]
Mahmoud, A. A. and Megahed, A. I. M. 2006 Effects of suction and injection on MHD heat transfer in an electrically conducting fluid at a stretching vertical plate embedded in a porous medium with uniform free stream. Nuovo Cimento Soc. Ital. Fis. B. 121, 923–935. [5.1.9.9]
Mahmoud, M. A. A. 2011 Variable viscosity effect on free convection of a non-Newtonian powser-law fluid over a vertical cone in a porous medium with variable heat flux. European Phys. J. Plus 126, #5 [5.8]
Mahmoud, M. A. A. and Megahed, A. M. 2009 Variable thermal conductivity effect on MHD free-convection flow over a vertical full cone in a non-Newtonian saturated porous medium. Nuovo Cimento Soc. Ital. Fis. B. 124, 731–739. [5.8]
Makinde, O. D. and Moitsheki, R. J. 2008 On nonperturbative technique for thermal radiation effect on natural convection past a vertical plate embedded in a saturated porous medium. Math. Probl. Engng. #689074. [5.1.9.9]
Mansour, M. A. and El-Shaer, N. A. 2001 Radiative effects on magnetohydrodynamic natural convection flows saturated in porous media. J. Magn. Magn. Mater. 237, 327–341. [5.1.9.4]
Mansour, M. A. and Gorla, R. S. R. 2000a Thermal dispersion effects on non-Darcy natural convection with internal heat generation. Chem. Engng. Commun. 177, 177–181. [5.1.9.4]
Mansour, M. A. and Gorla, R. S. R. 2000c Radiative and thermal dispersion effects on non-Darcy natural convection. J. Porous Media 3, 267–272. [5.1.9.4]
Mansour, M. A., El-Anssary, N. F., Aly, A. and Gorla, R. S. R. 2010b Chemical reaction and magnetohydrodynamic effects on free convection flow past an inclined surface in a porous medium. J. Porous Media 13, 87–96.
Masuoka, T., Tanigawa, H., Tsuruta, T. and Izaki, H. 1995a Studies on the improvement of the performances of insulation layers with isothermal screens. Proc. 3rd. ASME/JSME Thermal Engineering Joint Conference, vol.3, pp. 333–338. [6.13.2]
Masuoka, T., Tohda, Y., Tsurota, Y. and Yasuda, Y. 1986 Buoyant plume above a concentrated heat source in stratified porous media (in Japanese). Trans JSME Ser. B, 2656–2662. [5.10.2]
McNabb, A. 1965 On convection in a porous medium. Proc. 2nd Australasian Conf. Hydraulics and Fluid Mech., University of Auckland, pp. C161-171. [5.12.3]
Mealey, L. and Merkin, J. H. 2008 Free convection boundary layers on a vertical surface in a heat-generating porous medium. IMA J. Appl. Math. 73, 231–253. [5.1.9.4]
Mehmood, A. 2008 Analytical solution of three-dimensional viscous flow and heat transfer over a stretching flat surface by homotopy analysis method. ASME J. Heat Transfer 130, #121701. [5.2]
Mehta, K. N. and Rao, K. N. 1994 Buoyancy induced flow of non-Newtonian fluids over a non-isothermal horizontal plate embedded in a porous medium. Int. J. Engng Sci. 32, 521–525. [5.2]
Mehta, K. N. and Sood, S. 1992a Transient free convective flow about a non-isothermal vertical flat plate immersed in a saturated inhomogeneous porous medium. Int. Comm. Heat Mass Transfer 19, 687–699. [5.1.3]
Mehta, K. N. and Sood, S. 1992b Transient free convective flow with temperature dependent viscosity in a fluid saturated porous medium. Int. J. Engng Sci. 30, 1083–1087. [5.1.9.9]
Mehta, K. N. and Sood, S. 1994 Free convection about axisymmetric bodies immersed in inhomogeneous porous medium. Int. J. Engng Sci. 32, 945–953. [5.9]
Méndez, F., Luna, E., Treviño, C. and Pop, I. 2004 Asymptotic and numerical transient analysis of the free convection cooling of a vertical plate embedded in a porous medium. Heat Mass Transfer 40, 593–602. [5.1.5]
Merkin, J. H. 1978 Free convection boundary layers in a saturated porous medium with lateral mass flux. Int. J. Heat Mass Transfer 21, 1499–1504. [5.1.2, 5.5.1]
Merkin, J. H. 1979 Free convection boundary layers on axisymmetric and two-dimensional bodies of arbitrary shape in a saturated porous medium. Int. J. Heat Mass Transfer 22, 1461–1462. [5.5.1, 5.6.1, 5.9]
Merkin, J. H. 1986 Free convection from a vertical cylinder embedded in a saturated porous medium. J. Acta Mech. 62, 19–28. [5.7]
Merkin, J. H. 2008 Free convective boundary-layer flow in a heat-generating porous medium: Similarity solutions. Q. J. Mech. Appl. Math. 61, 205–218. [5.1.9.4]
Merkin, J. H. 2009 Natural convective boundary-layer flow in a heat generating porous medium with prescribed wall heat flux. ZAMP 60, 543–564. [5.1.9.4]
Merkin, J. H. and Kumaran, V. 2011 Free convection stagnation-point boundary-layer flow in a porous medium with a density maximum. Int. J. Therm. Sci. 50, 2176–2183. [5.1.9.9]
Merkin, J. H. and Mahmood, T. 1998 Convective flows on reactive surfaces in porous media. Transport Porous Media 33, 279–293. [3.4, 5.12.3]
Merkin, J. H. and Needham, D. J. 1987 The natural convection flow above a heated wall in a saturated porous medium. Q. J. Mech. Appl. Math. 40, 559–574. [5.1.9.9]
Merkin, J. H. and Pop, I. 1989 Free convection above a horizontal circular disk in a saturated porous medium. Wärme-Stoffübertrag. 24, 53–60. [5.12.3]
Merkin, J. H. and Pop, I. 2000 Free convection near a stagnation point in a porous medium resulting from an oscillatory wall temperature. Int. J. Heat Mass Transfer 43, 611–621. [5.5.1]
Merkin, J. H. and Pop, I. 2010 Natural convection boundary-layer flow in a porous medium with temperature-dependent boundary conditions. Transp. Porous Media 85, 397–414. [5.1.9.9]
Merkin, J. H. and Zhang, G. 1990a On the similarity solutions for free convection in a saturated porous medium adjacent to impermeable horizontal boundaries. Wärme-Stoffübertrag. 25, 179–184. [5.2]
Merkin, J. H. and Zhang, G. 1992 Boundary-layer flow past a suddenly heated vertical surface in a saturated porous medium. Wärme-Stoffübertrag. 27, 299–304. [5.1.3]
Minkowycz, W. J. and Cheng, P. 1976 Free convection about a vertical cylinder embedded in a porous medium. Int. J. Heat Mass Transfer 19, 805–813. [5.7]
Minkowycz, W. J. and Cheng, P. 1982 Local non-similar solutions for free convective flow with uniform lateral mass flux in a porous medium. Lett. Heat Mass Transfer 9, 159–168. [5.1.2]
Minkowycz, W. J., Cheng, P. and Moalem, F. 1985b Effect of surface mass transfer on buoyancy-induced Darcian flow adjacent to a horizontal heated surface. Int. Comm. Heat Mass Transfer 12, 55–65. [5.2]
Minto, B. J., Ingham, D. B. and Pop, I. 1998 Free convection driven by an exothermic reaction on vertical surface embedded in porous media. Int. J. Heat Mass Transfer 41, 11–23. [5.1.9.9]
Modather, M., Abdou, M. and El-Kabeir, S. M. M. 2007 Magnetohydrodynamics and radiative effects on free convection flow of fluid with variable viscosity from a vertical plate through a porous medium. J. Porous Media 10, 503–514.
Moghimi, M. A., Talbizadeh, P. and Mehrabian, M. A. 2011 Heat generation/absoption effects on magneto-hydrodynamic natural convection flow over a sphere in a non-Darcian porous medium. Proc. Inst. Mech. Engrs. E 225, 29–39. [5.6.1]
Mohamad, A. A. 2001 Natural convection from a vertical plate in a saturated porous medium: nonequilibrium theory. J. Porous Media 4, 181–186. [5.1.9.3]
Mohamed, R. A. and Abo-Dahab, S. M. 2009 The influence of chemical reaction and thermal radiation in the heat and mass transfer in MHD microplar flow over a vertical moving porous plate in a porous medium with heat generation. Int. J. Therm. Sci. 48, 1800–1813. [5.1.9.4s]
Mohamed, R. A., Abo-Dahab, S. M. and Nafal, T. A. 2010 Thermal radiation and MHD effectson free convective flow in a polar fluid through a porous medium in the presenjce of internal heat generaation and chemical reaction. Math. Prob. Engng. #804719. [5.1.9.4]
Mohammadein, A. A., Mansour, M. A., Abd el Gaied, S. M. and Gorla, R. S. R. 1998 Radiative effect on natural convection flows in porous media. Transport Porous Media 32, 263–283. [5.1.9.4]
Mohammadien, A. A. and El-Amin, M. F. 2000 Thermal dispersion-radiation effects on non-Darcy natural convection in a fluid saturated porous medium. Transport Porous Media 40, 153–163. [5.1.9.4]
Mohammadien, A. A. and El-Amin, M. F. 2001 Thermal radiation effects on power-law fluids over a horizontal plate embedded in a porous medium. Int. Comm. Heat Mass Transfer 27, 1025–1035. [5.2]
Muhaimin, I., Kandaswamy, R., Hashim, I. and Khamis, A. B. 2010b Local nonsimilarity solution on MHD convective heat transfer flow past a porous wedge in the presence of suction/injection. J. Porous Media 13, 487–495.
Mukhopadhyay, S. 2008 Natural convection flow on a sphere through porous medium in presence of heat source/sink near a stagnation point. Math. Modell. Anal. 13, 513–520. [5.6.1]
Murthy, P. V. S. N. and Singh, P. 1997a Effects of viscous dissipation on a non-Darcy natural convection regime. Int. J. Heat Mass Transfer 40, 1251–1260. [5.1.9.4]
Na, T. Y. and Pop, I. 1996 A note to the solution of Cheng-Minkowycz equation arising in free convection in porous media. Int. Comm. Heat Mass Transfer 23, 697–703. [5.1.9.9]
Nakayama, A. 1993a A similarity solution for free convection from a point heat source embedded in a non-Newtonian fluid-saturated porous medium. ASME J. Heat Transfer 115, 510–513. [5.11.1]
Nakayama, A. 1993b Free convection from a horizontal line heat source in a power-law fluid-saturated porous medium. Int. J. Heat Fluid Flow 14, 279–283. [5.10.1.2, 8.1.5]
Nakayama, A. and Hossain, M. A. 1994 Free convection in a saturated porous medium beyond the similarity solution. Appl. Sci. Res. 52, 133–145. [5.1.9.9]
Nakayama, A. and Koyama, H. 1987a Free convective heat transfer over a nonisothermal body of arbitrary shape embedded in a fluid-saturated porous medium. ASME J. Heat Transfer 109, 125–130. [5.9]
Nakayama, A. and Koyama, H. 1987c Effect of thermal stratification on free convection within a porous medium. AAIA J. Thermophys. Heat Transfer 1, 282–285. [5.1.4]
Nakayama, A. and Koyama, H. 1989 Similarity solutions for buoyancy induced flows over a non-isothermal curved surface in a thermally stratified porous medium. Appl. Sci. Res. 46, 309–323. [5.9]
Nakayama, A. and Koyama, H. 1991 Buoyancy-induced flow of non-Newtonian fluids over a non-isothermal body of arbitrary shape in a fluid-saturated porous medium. Appl. Sci. Res. 48, 55–70. [5.9]
Nakayama, A. and Pop, I. 1989 Free convection over a non-isothermal body in a porous medium with viscous dissipation. Int. Comm. Heat Mass Transfer 16, 173–180. [5.9]
Nakayama, A., Kokudai, T. and Koyama, H. 1988 Integral method for non-Darcy free convection over a vertical flat plate and cone embedded in a fluid-saturated porous medium. Wärme-Stoffübertrag. 23, 337–341. [5.8]
Nakayama, A., Koyama, H. and Kuwahara, F. 1989 Similarity solution for non-Darcy free convection from a non-isothermal curved surface in a fluid-saturated porous medium. ASME J. Heat Transfer 111, 807–811. [5.9]
Nakayama, A., Koyama, H. and Kuwahara, F. 1991 A general transformation for transient non-Darcy free and forced convection within a fluid-saturated porous medium. Proc. ASME/JSME Thermal Engineering Joint Conference —1991, vol. 4, pp. 287–293. [ 5.9]
Nazar, R., Arafin, N. M. and Pop, I. 2006 Free convection boundary layer flow over vertical and horizontsl flat surfaces embedded in a porous medium under mixed thermal boundary conditions. Int.Comm. Heat Mass Transfer 33, 87–93. [5.1.9.8]
Ngo, C. C. and Lai, F. C. 2009 Heat transfer analysis of soil heating systems. Int. J. Heat Mass Transfer 52, 6021–6027. [5.5.1]
Nguyen, H. D., Paik, S., Douglass, R. W. and Pop, I. 1996 Unsteady non-Darcy reaction-driven flow from an anisotropic cylinder in porous media. Chem. Engng. Sci. 51, 4963–4977. [5.5.1]
Nield, D. A. 1994c Estimation of an effective Rayleigh number for convection in a vertically inhomogeneous porous medium or clear fluid. Int. J. Heat Fluid Flow 15, 337–340. [5.4, 6.7, 6.13.2]
Nield, D. A. and Kuznetsov, A. V. 2008b Natural convection about a vertical plate embedded in a bidisperse porous medium. Int. J. Heat Mass Transfer 51, 1658–1664. 5.1.9.9]
Nield, D. A. and Kuznetsov, A. V. 2011c The Cheng-Minkowycz problem for natural convection about a vertical plate embedded in a tri-disperse porous medium. Int. J. Heat Mass Transfer 54, 3505–3513. [5.1.9.4]
Nield, D. A. and White, S. P. 1982 Natural convection in an infinite porous medium produced by a line heat source. Mathematics and Models in Engineering Science (ed. A. McNabb et al.) Dept. Sci. Indust. Res., Wellington, New Zealand, pp. 121–128. [5.10.2]
Nilson, R. H. 1981 Natural convective boundary layer on two-dimensional and axisymmetric surfaces in high-Pr fluids or in fluid saturated porous media. ASME J. Heat Transfer 103, 803–807. [5.6.1]
Noor, N. F. M. and Hashim, I. 2010 MHD viscous flow over a linearly stretching sheet embedded in a non-Darcian porous medium. J. Porous Media 13, 349–355. [5.1.9.9]
Pal, D. and Hiremath, P. S. 2010 Computational modeling of heat transfer over an unsteady stretching surface embedded in a porous medium. Meccanica 45, 415–424. [5.1.9.9]
Pantokratoras, A. 2006 Natural convection of air and water with variable thermophysical properties about a vertical isothermal flat plate embedded in a Darcy porous medium. Prog. Comput. Fluid Dyn. 6, 498–510. [5.1.9.9]
Pantokratoras, A. 2007a Fully developed Couette flow of three fluids with variable thermophysical properties flowing through a porous medium channel heated asymmetrically with large temperature difference. ASME J. Heat Transfer 129, 1742–1747. [4.16.1]
Pantokratoras, A. 2007b Fully developed forced convection of three fluids with variable thermophysical properties flowing through a porous medium chmnnel heated asymmetrically with large temperature differences. J. Porous Media 10, 409–419. [4.16.1]
Pantokratoras, A. 2008 Comment on “Unsteady MHD combined convection over a moving vertical sheet in a fluid saturated porous medium with uniform surface heat flux”, S.S.M. El-Kabeir, A. M. Rashad, Rama Subba Reddy Gorla, Mathematical and Computer Modelling 46 (2007) 384–397. Math. Comput. Modelling 48, 662–663. [8.1.6]
Pantokratoras, A. 2009a Comments on “Perturbation analysis of radiative effect on free convection flows in porous medium in presence of pressure work and dissipation, by A. M. Rashad [Commun. Nonlinear Sci. Numer. Simul. 2009: 14: 140–153]. Commun. Nonlinear Sci. Numer. Simul. 14, 345–346. [5.1.9.4]
Pascal, H. 1990 Rheological effects of non-Newtonian fluids on natural convection in a porous medium. [5.1.9.2]
Pascal, J. P. and Pascal, H. 1997 Free convection in a non-Newtonian fluid saturated porous medium with lateral mass flux. Int. J. Non-Linear Mech. 32, 471–482. [5.7]
Patil, P. M. 2008 Effects of free convection on the oscillatory flow of a polar fluid through a porous medium in presence of variable heat flux. J. Engng. Phys. Thermophys. 81, 905-922. [5.1.9.2]
Peng, C., Zeng, T. and Cheng, G. 1992 Free convection about vertical needles embedded in a saturated porous medium. AIAA J. Thermophys. Heat Transfer 6, 558–561. [5.12.1]
Plumb, O. A. 1983 The effect of thermal dispersion on heat transfer in packed bed boundary layers. Proc. ASME JSME Thermal Engineering Joint Conference 2, 17–22. [5.1.7.3]
Plumb, O. A. and Huenefeld, J. C. 1981 Non-Darcy natural convection from heated surfaces in saturated porous media. Int. J. Heat Mass Transfer 24, 765–768. [5.1.7.2, 5.1.8]
Pop, I. 2004 Some boundary-layer problems in convective flows. In Emerging Technologies and Techniques in Porous Media (D. B. Ingham, A. Bejan, E. Mamut and I. Pop, eds), Kluwer Academic, Dordrecht, pp. 65–91. [5]
Pop, I. 2011 Reply to the Paper TIPM1512: Note on the “Scaling transformations for boundary layer flow near the stagnation point on a heated permeable stretching surface in a porous medium saturated with a anofluid and heat generation/absorption effects.” by E. Magyari.Transp. Porous Media 87, 49–51.[5.1.9.9]
Pop, I. and Cheng, P. 1986 An integral solution for free convection of a Darcian fluid about a cone with curvature effects. Int. Comm. Heat Mass Transfer 13, 433–438. [5.8]
Pop, I. and Gorla, R. S. R. 1991 Horizontal boundary-layer natural convection in a porous medium saturated with a gas. Transport in Porous Media 6, 159–171. [5.2]
Pop, I. and Herwig, H. 1992 Free convection from a vertical surface in a porous medium saturated with fluids of variable properties: an asymptotic approach. Heat and Mass Transfer in Porous Media (ed. M. Quintard and M. Todorovic), Elsevier, Amsterdam, 337–348. [5.1.9.9]
Pop, I. and Ingham, D. B. 1990 Natural convection about a heated sphere in a porous medium. Heat Transfer 1990, Hemisphere, New York, vol, 2, pp. 567–572. [5.6.2, 5.6.3]
Pop, I. and Ingham, D. B. 2000 Convective boundary layers in porous media: external flows. Handbook of Porous Media (K. Vafai, ed.), Marcel Dekker, New York., pp. 313–356. [5]
Pop, I. and Ingham, D. B. 2001 Convection Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Elsevier, Oxford. [5]
Pop, I. and Merkin, J. H. 1995 Conjugate free convection on a vertical surface in a saturated porous medium. Fluid Dyn. Res. 16, 71–86. [5.1.5]
Pop, I. and Na, N. Y. 1994 Natural convection of a Darcian fluid about a wavy cone. Int. Comm. Heat Mass Transfer, 21, 891–899. [5.8]
Pop, I. and Na, T. Y. 1995 Natural convection over a frustum of a wavy cone in a porous medium. Mech. Res. Comm. 22, 181–190. [5.8]
Pop, I. and Na, T. Y. 1997 Free convection from an arbitrarily inclined plate in a porous medium. Heat Mass Transfer 32, 55–59. [5.3]
Pop, I. and Na, T. Y. 2000 Conjugate free convection over a vertical slender hollow cylinder embedded in a porous medium. Heat Mass Transfer 36, 375–379. [5.7]
Pop, I. and Nakayama, A. 1994 Conjugate free convection from long vertical plate fins in a non-Newtonian fluid-saturated porous medium. Int. Comm. Heat Mass Transfer 21, 297–305. [5.12.1]
Pop, I. and Nakayama, A. 1999 Conjugate free and mixed convection heat transfer from vertical fins embedded in porous media. In Recent advances in Analysis of Heat Transfer for Fin Type Surfaces (B. Sunden and P. J. Heggs, eds.), Computational Mechanics Publications, Southampton, pp. 67–96. [5.12.1]
Pop, I., Angirasa, D. and Peterson, G. P., 1997 Natural convection in porous media near L-shaped corners. Int. J. Heat Mass Transfer 40, 485–490. [5.12.2]
Pop, I., Cheng, P. and Le, T. 1989 Leading edge effects on free convection of a Darcian fluid about a semi-infinite vertical plate with uniform heat flux. Int. J. Heat Mass Transfer 32, 493–501. [5.1.6]
Pop, I., Harris, S. D., Ingham, D. B. and Rhea, S. 2003 Three-dimensional stagnation point free convection on a reactive surface in a porous medium. Int. J. Energy Res. 27, 919–939. [5.12.3]
Pop, I., Ingham D. B. and Bradean, R. 1996 Transient free convection about a horizontal circular cylinder in a porous medium with constant surface flux heating, Acta Mech. 119, 79–91. [5.5.1]
Pop, I., Ingham, D. B. and Cheng, P. 1993a Transient free convection about a horizontal circular cylinder in a porous medium. Fluid Dyn. Res., 12, 295–305. [5.5.1]
Pop, I., Ingham, D. B. and Merkin, J. H. 1998 Transient convection heat transfer in a porous medium: External flows. Transport Phenomena in Porous Media (eds. D.B. Ingham and I. Pop), Elsevier, Oxford, pp. 205–232. [5.1.3]
Pop, I., Ingham, D. B., Heggs, P. J. and Gardner, D. 1986 Conjugate heat transfer from a downward projecting fin immersed in a porous medium. Heat Transfer 1986, Hemisphere, Washington, DC, 5, 2635–2640. [5.12.1]
Pop, I., Kumari, M. and Nath, G. 1992b Free convection about cylinders of elliptic cross section embedded in a porous medium. Int. J. Engng Sci. 30, 35–45. [5.5.1]
Pop, I., Lesnic, D. and Ingham, D. B. 2000 Asymptotic solutions for the free convection boundary layer flow along a vertical surface in a porous medium with Newtonian heating. Hybrid Methods in Engineering 2, 31–40. [5.1.9.8]
Pop, I., Merkin, J. H. and Ingham, D. B. 2002 Chemically driven convection in porous media. In Transport Phenomena in Porous Media II (D. B. Ingham and I. Pop, eds.) Elsevier, Oxford, pp. 341–364. [5.12.3]
Pop, I., Rees, D. A. S. and Storesletten, L. 1998 Free convection in a shallow annular cavity filled with a porous medium. Journal of Porous Media 1, 227–241. [7.3.3]
Pop, I., Sunada, J. K., Cheng, P. and Minkowycz, W. J. 1985 Conjugate free convection from long vertical plate fins embedded in a porous medium at high Rayleigh numbers. Int. J. Heat Mass Transfer 28, 1629–1636. [5.12.1]
Postelnicu, A. 2007b Effects of thermophoresis particle deposition in free convection boundary layer from a horizontal flat plate embedded in a porous medium. Int. J. Heat Mass Transfer 50, 2981–2985. [5.2]
Postelnicu, A. and Pop, I. 1999 Similarity solutions of free convection boundary layers over vertical and horizontal surfaces in porous media with internal heat generation. Int. Comm. Heat Mass Transfer 26, 1183–1191. [5.1.9.4]
Postelnicu, A., Grosan, T. and Pop, I. 2000 Free convection boundary-layer over a vertical permeable flat plate in a porous medium with internal heat generation. Int. Comm. Heat Mass Transfer 27, 729–738. [5.1.9.4]
Postelnicu, A., Grosan, T. and Pop, I. 2001 The effect of variable viscosity on forced convection flow past a horizontal flat plate in a porous medium with internal heat generation. Mech. Res. Comm. 28, 331–337. [5.2]
Postelnicu, A., Magyari, E. and Pop, I. 2009 The effect of uniform horizontal throughflow on the Darcy free convection over a permeable vertical plate with volumetric heat generation.. Transp. Porous Media 80, 101–115. [5.1.9.4]
Prasad, K. V., Vajravelu, K. and van Gorder, R. A. 2011 Non-Darcian flow and heat transfer along a permeable vertical surface with nonlinear density temperature variation. Acta Mech. 220, 139–154. [5.1.9.9]
Purushothaman, R., Ganapathy, R. and Hiremath, P. S. 1990 Free convection in an infinite porous medium due to a pulsating point heat source. Z. Angew. Math. Mech. 70, 41–47. [5.11.2]
Rabadi, N. J. and Hamdan, E. M. 2000 Free convection from inclined permeable walls embedded in variable permeability porous media with lateral mass flux. J. Petrol. Sci. Engng. 26, 241–251. [5.3]
Rahman, M. M. and Sattar, M. A. 2006 Magnetohydrodynamic convective flow of a micropolar fluid past a continuously moving porous plate in the presence of heat generation/absoption. ASME J. Heat Transfer 128, 142–152. [5.1.9.9]
Rahman, S. U. 1999 An experimental study on buoyancy-driven convective mass transfer from spheres embedded in saturated porous media. Heat Mass Transfer 35, 487–491. [5.6.1]
Rahman, S. U. and Badr, H. M. 2002 Natural convection from a vertical wavy surface embedded in saturated porous media. Ind. Engng. Chem. Res. 41, 4422–4429. [5.1.8]
Rahman, S. U., Al-Slaeh, M. A. and Sharma, R. N. 2000 An experimental study on natural convection from heated surfaces embedded in porous media. Indust. Engng. Chem. Res. 39, 214–218. [5.1.8]
Ramaniah, G. and Malarvizhi G. 1991 Note on exact solutions of certain non-linear boundary value problems governing convection in porous media. Int. J. Non-linear Mech. 26, 345–347. [5.1.9.9, 5.2]
Ramaniah, G. and Malarvizhi G. 1994 Note on the boundary value problem arising in free convection in porous media. Int. J. Engng Sci. 32, 2011–2013. [5.1.9.9]
Rao, K.N. and Pop, I. 1994 Transient free convection in a fluid saturated porous medium with temperature dependent viscosity. Int. Comm. Heat Mass Transfer 21, 573–591. [5.1.9.9]
Raptis, A. 1998 Radiation and free convection flow through a porous medium. Int. Comm. Heat Mass Transfer 25, 289–295. [5.1.9.4]
Raptis. A. and Perdikis, C. 2004 Unsteady flow through a highly porous medium in the presence of radiation. Transport Porous Media 57, 171–179 [5.1.9.4]
Rashad, A. M. 2008 Influence of radiation on MHD free convection from a vertical flat plate embedded in porous media with thermophoretic deposition of particles. Commun. Nonliner Sci. Numer. Simul. 13, 2213–2222. [5.1.9.9]
Rashad, A. M. 2009a Perturbation analysis of radiative effect on free convection flows in porous medium in presence of pressure work and dissipation Commun. Nonlinear Sci. Numer. Simul. 14, 140–153. [5.1.9.4]
Rashad, A. M. 2009b Reponse to the comments of Asterios Pantokratoras on “Perturbation analysis of radiative effect on free convection flows in porous medium in presence of pressure work and dissipation.” Commun. Nonlinear Sci. Numer. Simul. 14, 347–349. [5.1.9.4]
Ratish Kumar, B. V. and Singh, P. 1998 Effect of thermal stratification on free convection in a fluid-saturated porous enclosure. Numer. Heat Transfer A 34, 343–356. [5.1.4]
Rees, D. A. S. 1993 Numerical investigation of the nonlinear wave stability of vertical thermal boundary layer flow in a porous medium. Z. Angew. Math. Phys. 44, 306–313. [5.1.9.9]
Rees, D. A. S. 1996a The effect of inertia on free convection from a horizontal surface embedded in a porous medium. Int. J. Heat Mass Transfer 39, 3425–3430. [5.2]
Rees, D. A. S. 1997b Three-dimensional free convective boundary layers in porous media induced by a heated surface with spanwise temperature gradient. ASME J. Heat Transfer 119, 792–798. [5.2} [5.1.9.9]
Rees, D. A. S. 1998 Thermal boundary layer instabilities in porous media: a critical review. Transport Phenomena in Porous Media (eds. D.B. Ingham and I. Pop), Elsevier, Oxford, pp. 233–259. [5.4]
Rees, D. A. S. 1999 Free convective boundary-layer flow from a heated surface in a layered porous medium J. Porous Media 2, 39–58. [5.1.9.5]
Rees, D. A. S. 2001 Vortex instability from a near-vertical heated surface in a porous medium. I. Linear instability. Proc. Roy. Soc. Lond. A 457, 1721–1734. [5.4]
Rees, D. A. S. 2002a Vortex instability from a near-vertical heated surface in a porous medium. II. Nonlinear evolution. Proc. Roy. Soc. Lond. A 458, 1773–1782. [5.4]
Rees, D. A. S. 2002c Recent advances in the instability of free convective boundary layers in porous media. In Transport Phenomena in Porous Media II (D. B. Ingham and I. Pop, eds.), Elsevier, Oxford, pp. 54–81. [5.4]
Rees, D. A. S. 2003 Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model: elliptical effects. Z. Angew. Math. Phys. 54, 437–448. [5.1.9.3]
Rees, D. A. S. 2004b Nonlinear vortex instabilities in free convective boundary layers in porous media. In Emerging Technologies and Techniques in Porous Media (D. B. Ingham, A. Bejan, E. Mamut and I. Pop, eds), Kluwer Academic, Dordrecht, pp. 235–245. [5.4]
Rees, D. A. S. 2009b The onset and nonlinear development of vortex instabilities in a horizontal forced convection boundary layer with uniform surface suction. Transp. Porous Media 77, 243–265. [5.4]
Rees, D. A. S. and Bassom, A. P. 1991 Some exact solutions for free convective flows over heated semi-infinite surfaces in porous media. Int. J. Heat Mass Transfer 34, 1564–1567. [5.8]
Rees, D. A. S. and Bassom, A. P. 1993 The nonlinear non-parallel wave instability of boundary-layer flow induced by a horizontal heated surface in porous media. J. Fluid Mech. 253, 267–295. [5.2]
Rees, D. A. S. and Bassom, A. P. 1994 The linear wave instability of boundary layer flow induced by a horizontal heated surface in porous media. Int. Comm. Heat Mass Transfer 21, 143–150. [5.2]
Rees, D. A. S. and Hossain, M. A. 1999 Combined effect of inertia and a spanwise pressure gradient on free convection from a vertical surface in porous media. Numer. Heat Transfer A 36, 725–736. [5.1.7.2]
Rees, D. A. S. and Hossain, M. A. 2001 The effect of inertia on free convective plumes in porous media. Int. Comm. Heat Mass Transfer 28, 1137–1142. [5.10.1.2]
Rees, D. A. S. and Pop, I. 1994a A note on free convection along a vertical wavy surface in a porous medium. ASME J. Heat Transfer 116, 505–508. [5.1.9.6]
Rees, D. A. S. and Pop, I. 1994b Free convection induced by a horizontal wavy surface in a porous medium. Fluid Dyn. Res. 14, 151–166. [5.2]
Rees, D. A. S. and Pop, I. 1995a Free convection induced by a vertical wavy surface with uniform heat flux in a porous medium. ASME J. Heat Transfer 117, 547–550. [5.1.9.6]
Rees, D. A. S. and Pop, I. 1995b Non-Darcy natural convection from a vertical wavy surface in a porous medium. Transport in Porous Media 20, 223–234. [5.1.9.6]
Rees, D. A. S. and Pop, I. 1997 The effect of longitudinal surface waves on free convection from vertical surfaces in porous media. Int. Comm. Heat Mass Transfer 24, 419–425. [5.1.9.6]
Rees, D. A. S. and Pop, I. 1999 Free convective stagnation-point flow in a porous medium using a thermal nonequilibrium model. Int. Comm. Heat Mass Transfer 26, 945–954. [5.1.9.3, 5.12.3]
Rees, D. A. S. and Pop, I. 2000a Vertical free convection in a porous medium with variable permeability effects. Int. J. Heat Mass Transfer 43, 2565–2571. [5.1.9.5]
Rees, D. A. S. and Pop, I. 2000b The effect of g-jitter on vertical free convection boundary-layer flow in porous media. Int. Comm. Heat Mass Transfer 27, 415–424. [5.1.9.7]
Rees, D. A. S. and Pop, I. 2000c Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model. J. Porous Media 3, 31–44. [5.1.9.3]
Rees, D. A. S. and Pop, I. 2001 The effect of g-jitter on free convection near a stagnation point in a porous medium. Int. J. Heat Mass Transfer 44, 877–883. [5.12.3]
Rees, D. A. S. and Pop, I. 2002 Comments on ‘Natural convection from a vertical plate in a saturated porous medium : nonequilibrium theory’ by A. A. Mohamad. J. Porous Media 5, 225–227. [5.1.9.3]
Rees, D. A. S. and Pop, I. 2003 The effect of large-amplitude g-jitter vertical free convection boundary-layer flow in porous media. Int. J. Heat Mass Transfer 46, 1097–1102. [5.1.9.7]
Rees, D. A. S. and Pop, I. 2005 Local thermal non-equilibrium in porous media convection. In Transport Phenomena in Porous Media III, (eds. D. B. Ingham and I. Pop), Elsevier, Oxford, pp. 147–173. [5.1.9.3]
Rees, D. A. S. and Pop, I. 2010 Discussion on the paper : Vortex instabiltiy of mixed convection boundary layer flow adjacent to a non-isothermal horizontal surface in a porous medium with variable permeability. J. Porous Media 13, 945–949. [5.4]
Rees, D. A. S. and Riley, D. S. 1985 Free convection above a near horizontal semi-infinite heated surface embedded in a saturated porous medium. Int. J. Heat Mass Transfer 28, 183–190. [5.3]
Rees, D. A. S. and Storesletten, L. 1995 The effect of anisotropic permeability on free convective boundary layer flow in porous media. Transport in Porous Media 19, 79–92. [5.1.9.5]
Rees, D. A. S. and Storesletten, L. 2002 The linear stability of a thermal boundary layer with suction in an anisotropic porous medium. Fluid Dyn. Res. 30, 155–168. [5.3]
Rees, D. A. S. and Vafai, K. 1999 Darcy-Brinkman free convection from a heated horizontal surface. Numer. Heat Transfer A 35, 191–204. [5.2]
Rees, D. A. S., Bassom, A. P. and Pop, I. 2003a Forced convection past a heated cylinder in a porous medium using a thermal non-equilibrium model: boundary layer analysis. European J. Mech. B 22, 473–476. [5.1.9.3, 5.7]
Rees, D. A. S., Magyari, E. and Keller, B. 2003b The development of the asymptotic viscous dissipation profile in a vertical free convective boundary layer flow in a porous medium. Transport Porous Media 53, 347–355. [5.1.9.4]
Rees, D. A. S., Magyari, E., Keller, B. 2005a Vortex instability of the asymptotic dissipation profile in porous media. Transport Porous Media 61, 1–14. [5.1.9.4, 6.6]
Rees, D. A. S., Nield, D. A. and Kuznetsov, A. V. 2008b Vertical free convective boundary-layer flow in a bidisperse porous medium. ASME J. Heat Transfer 130, #092601. [5.1.9.9]
Rees, D. A. S., Postelnicu, A. and Bassom, A. P. 2008c The linear vortex instability of the near-vertical line source plume in porous media. Transp. Porous Media 74, 221–238. [5.10.1.1]
Rees, D. A. S., Storesletten, L. and Bassom, A. P. 2002 Convective plume paths in anisotropic porous media. Transport Porous Media 49, 9–25. [5.10.1.1]
Riley, D. S. and Rees, D. A. S. 1985 Non-Darcy natural convection from arbitrarily inclined heated surfaces in saturated porous media. Q. J. Mech. Appl. Math. 38, 277–295. [5.12.2]
Rosali, H., Ishak, A. and Pop, I. 2012 Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction. Int. Comm. Heat Mass Transfer 39, 826–829. [5.1.9.2]
Saeid, N. F. and Mohamad, A. A. 2005a Periodic free convection from a vertical plate in a saturated porous medium, non-equilibrium model. Int. J. Heat Mass Transfer 48, 3855–3863. [5.1.9.7]
Saied, N. H. 2007 Conjugate natural convection in a porous enclosure: effect of conduction in one of the vertical walls. Int. J. Thermal Sci. 46, 531–539. [7.1.5]
Sajid, M., Ahmad, I. and Hayat, T. 2009 Unsteady boundary layer flow due to a stretching sheet in a porous medium with partial slip. J. Porous Media 12, 911–917. [5.1.9.9]
Salama, A., El-Amin, M. F., Abbas, I. and Sun, S. Y. 2011 On the viscous dissipation modeling of thermal fluid flow in a porous medium Arkiv. Appl. Mech. 81, 1865–1878. [5.1.9. 9]
Salem, A. M. 2009 Temperature-dependent viscosity effects on non-Darcy hydromagnetic free-convection heat transfer from a vertical wedge in porous media. Nouvo Cim. Soc. Ital. Fis. B 124, 959–974. [5.3]
Salem, A. M. 2010 Temperature-dependent viscosity effects on non-Darcy hydrodynamic free convection heat transfer from a vertical wedge in porous media. Chinese Phys. Lett. 27, #064401. [5.3]
Sano, T. 1996 Unsteady forced and natural convection around a sphere immersed in a porous medium. J. Engng Math. 30, 515–525. [5.6.2]
Sano, T. and Okihara, R. 1994 Natural convection around a sphere immersed in a porous medium at small Rayleigh numbers. Fluid Dyn. Res. 13, 39–44. [5.6.2]
Seddeek, M. A. 2007 Chebyshev finite differences method for hydromagnetic free convection from a cone and a wedge through porous media with radiation. J. Porous Media 10, 99–108; erratum p. 420. [5.8]
Seetharamu, K. N. and Dutta, P. 1990 Free convection in a saturated porous medium adjacent to a non-isothermal vertical impermeable wall. Wärme-Stoffübertrag. 25, 9–15. [5.1.9.9]
Senapati, N. and Dhal, R. K. 2011 MHD free convective flow past an exponentially accelerated vertical plate through porous medium with diffusion of chemically reactive species. Proc. Nat. Acad. Sci. Indai A 81, 39–48. [5.1.9.9]
Seyf, H. R. and Layeghi, M. 2010 Numerical analysis of convective heat transfer from an elliptical pin fin heat sink with and without metal foam insert. ASME J. Heat Transfer 132, #071401. [5.12.1]
Shakeri, E., Nazari, M. and Kayhani, M. H. 2012 Free convection heat transfer over a vertical cylinder in a saturated porous medium using a local thermal non-equilibrium model. Transp. Porous Media 93, 453–460. [5.7]
Shantha, G. and Shanker, B. 2010 Free convective flow of a conducting couple stress fluid in a porous medium: A state space approach. Int. J. Numer. Meth. Heat Fluid Flow 20, 250–264. [5.1.9.2]
Shenoy, A. V. 1992 Darcy natural, forced and mixed convection heat transfer from an isothermal vertical flat plate in a porous medium saturated with an elastic fluid of constant viscosity. Int. J. Engng Sci. 30, 455–467. [4.12.3, 5.1.9.2, 8.1.1]
Shenoy, A. V. 1993a Darcy-Forchheimer natural, forced and mixed convection heat transfer in non-Newtonian power-law fluid-saturated porous media. Transport in Porous Media 11, 219–241. [4.16.3, 5.1.9.2, 8.1.1]
Shu, J. J. and Pop, I. 1997 Inclined wall plumes in porous media. Fluid Dyn. Res. 21, 303–317. [5.3]
Shu, J. J. and Pop, I. 1998 Transient conjugate free convection from a vertical flat plate in a porous medium subjected to a sudden change in surface heat flux. Int. J. Engng. Sci. 36, 207–214. [5.1.5]
Singh, A. K. 2008 Three-dimensional free convection flow of a viscous fluid through a nonhomogeneous porous medium. J. Porous Media 11, 603–615. [5.1.9.9]
Singh, A. K., Agnihotri, P., Singh, N. P. and Singh, A. K. 2011a Transient and non-Darcian effects on natural convection flow in a vertical channel partially filled with porous medium: Analysis with Forchheimer-Brinkman extended Darcy model. Int. J. Heat Mass Transfer 54, 1111–1120. [7.7]
Singh, A. K., Singh, H., Singh, U. and Singh, N. P. 2011b Hydromagnetic convection boundary layer flow caused by stretching a porous wall embedded within porous medium. Proc. Nat. Acad. Sci. Indai A 81, 59–64. [5.1.9.9]
Singh, P. and Tewari, K. 1993 Non-Darcy free convection from vertical surfaces in thermally stratified porous media. Int. J. Engng Sci. 31, 1233–1242. [5.1.4]
Singh, P., Misra, J. K. and Narayan, K. A. 1988 Three-dimensional convective flow and heat transfer in a porous medium. Indian J. Pure Appl. Math. 19, 1130–1135. [5.1.9.9]
Singh, T. and Gorla, M. G. 2010 Three-dimensional MHD flow and heat transfer through porous medium bounded by a porous vertical surface with heat source and variable permeability. Proc. Nat. Acad. Sci. India A 80, 369–375. [5.1.9.9]
Sohouli, A. R., Domairry, D., Famouri, M. and Mohsenzadeh,A. 2008 Analytical solution of natural convection of Darcian fluid about a vertical full cone embedded in porous media prescribed wall temperature by means of HAM. Int. Comm. Heat Mass Transfer 35, 1380–1384. [5.8]
Sun, Q. and Pop, I. 2011 Free convection in a triangle cavity filled with a porous medium saturated with nanofluids with flush mounted heater on wall. Int. J. Therm. Sci. 50, 2141–2153. [5.12.3]
Takatsu, Y., Masuoka, T., Hashimoto, Y. and Yokota, K. 1997 Natural convection along a vertical porous surface. Heat Transfer Japan. Res. 26, 385–397. [5.1.9.9]
Takhar, H. S., Chamkha, A. J. and Nath G. 2002 Natural convection on a vertical cylinder embedded in a thermally stratified high-porosity medium. Int. J. Thermal Sci. 41, 83–93. [5.7]
Takhar, H. S., Chamkha, A. J. and Nath G. 2003 Effects of non-uniform temperature or mass transfer in finite sections of an inclined plate on the MHD natural convection flow in a temperature stratified high-porosity porous medium. Int. J. Thermal Sci. 42, 829–836. [5.3]
Takhar, H. S., Kumari, M. and Bèg, O. A. 1998 Computational analysis of coupled radiation-convection dissipative non-gray gas flow in a non-Darcy gas flow in a non-Darcy porous medium using the Keller box implicit difference scheme. Int. J. Energy Res. 22, 141–159. [5.1.9.4]
Takhar, H. S., Roy, S. and Nath, G. 2003 Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents. Heat Mass Transfer 39, 825–834. [9.2.1]
Tamayol, A., Hooman, K. and Bahrami, M. 2010 Thermal analysis of flow in a porous medium over a permeable stretching wall. Transp. Porous Media 85¸ 661–676. [5.1.9.9]
Tewari, K. and Singh, P. 1992 Natural convection in a thermally stratified fluid-saturated porous medium. Int. J. Engng Sci. 30, 1003–1008. [5.1.4]
Tyvand, P. A. 1995 First-order transient free convection about a horizontal cylinder embedded in a porous medium. Fluid Dyn. Res. 15, 277–290. [5.5.1]
Vajravelu, K., Prasad, K. V., van Gorder, R. A. and Lee, J. 2011 Free convection boundary layer flow past a vertical surface in a porous medium with temperature-dependent properties. Transp. Porous Media 90, 977–992. [5.1.9.9]
Vasantha, R., Pop, I. and Nath, G. 1986 Non-Darcy natural convection over a slender vertical frustum of a cone in a saturated porous medium. Int. J. Heat Mass Transfer 29, 153–156. [5.8]
Vasseur, P. and Degan, G. 1998 Free convection along a vertical heated plate in a porous medium with anisotropic permeability. Int. J. Numer. Methods Heat Fluid Flow 8, 43–63. [5.1.9.5]
Vaszi, A. Z., Elliot, L., and Ingham, D. B. 2003 Conjugate free convection from vertical fins embedded in a porous medium. Numer. Heat Transfer A 44, 743–770. [5.1.5]
Vaszi, A. Z., Elliot, L., Ingham, D. B. and Pop, I. 2001a Conjugate free convection above a cooled finite horizontal flat plate embedded in a porous medium. Int. Comm. Heat Mass Transfer 28, 703–712. [5.2]
Vaszi, A. Z., Elliot, L., Ingham, D. B. and Pop, I. 2002a Conjugate free convection above a heated finite horizontal flat plate embedded in a porous medium. Int. J. Heat Mass Transfer 45, 2777–2795. [5.2]
Vaszi, A. Z., Elliot, L., Ingham, D. B. and Pop, I. 2002b Conjugate free convection from a vertical plate fin embedded in a porous medium. Heat Transfer 2002, Proc. 12th Int. Heat Transfer Conf., Elsevier, Vol. 2, pp. 827–832. [5.12.1]
Vaszi, A. Z., Ingham, D. B., Lesnic, D., Munslow, D. and Pop, I. 2001b Conjugate free convection from a slightly inclined plate embedded in a porous medium. Zeit. Angew. Math. Mech. 81, 465–479. [5.3]
Vedha-Nayagam, M., Jain, P. and Fairweather, G. 1987 The effect of surface mass transfer on buoyancy induced flow in a variable-porosity medium adjacent to a horizontal heated plate. Int. Comm. Heat Mass Transfer 14, 495–506. [5.2]
Vynnycky, M. and Kimura, S. 1994 Conjugate free convection due to a vertical plate in a porous medium. Int. J. Heat Mass Transfer 37, 229–236. [5.1.5]
Vynnycky, M. and Kimura, S. 1995 Transient conjugate free convection due to a vertical plate in a porous medium. Int. J. Heat Mass Transfer 38, 219–231. [5.1.5]
Wang, C., Zhu, J. M., Liao, S. J. and Pop, I. 2003c On the explicit analytic solution of Cheng-Chang equation. Int. J. Heat Mass Transfer 46, 1855–1860. [5.2]
Wang, S. C., Chen, C. K., Yang, Y. T. and Yang, Y. T. 2002 Natural convection of non-Newtonian fluids through permeable axisymmetric and two-dimensional bodies in a porous medium. Int. J. Heat Mass Transfer 45, 393–408. [5.9]
Wooding, R. A. 1963 Convection in a saturated porous medium at large Reynolds number or Péclet number. J. Fluid Mech. 15, 527–544. [5.10.1.1, 5.11.1]
Wooding, R. A. 1985 Convective plumes in saturated porous media. Convective Flows in Porous Media (eds. R. A. Wooding and I. White) Dept. Sci. Indust. Res., Wellington, N. Z., pp. 167–178. [5.11.1]
Wright, S. D., Ingham, D. B. and Pop, I. 1996 On natural convection from a vertical plate with a prescribed surface heat flux in porous media. Transport in Porous Media 22, 181–193. [5.1.1]
Xu, H. 2004 An explicit analytic solution for free convection about a vertical plate embedded in a porous medium by means of homotopy analysis method. Appl. Math. Comput. 158, 433–443. [5.1.1]
Yamamoto, K. 1974 Natural convection about a heated sphere in a porous medium. J. Phys. Soc. Japan 37, 1164–1166. [5.6.2]
Yan, B., Pop, I. and Ingham, D. B. 1997 A numerical study of unsteady free convection from a sphere in a porous medium. Int J. Heat Mass Transfer 40, 893–903. [5.6.1]
Yang, Y. T. and Wang, S. J. 1996 Free convection heat transfer of non-Newtonian fluids over axisymmetric and two-dimensional bodies of arbitrary shape embedded in a fluid-saturated porous medium. Int. J. Heat Mass Transfer 39, 203–210. [5.9]
Yih, K. A. 1997 The effect of transpiration on coupled heat and mass transfer in mixed convection over a vertical plate embedded in a saturated porous medium. Int. Comm. Heat Mass Transfer 24, 265–275. [9.6.1]
Yih, K. A. 1997 The effect of uniform lateral mass flux on free convection about a vertical cone embedded in a saturated porous medium. Int. Comm. Heat Mass Transfer 24, 1195–1205. [5.8]
Yih, K. A. 1998b Uniform lateral mass flux effect on natural convection on non-Newtonian fluids over a cone in porous media. Int. Comm. Heat Mass Transfer 25, 959–968. [5.8]
Yih, K. A. 1999e Coupled heat and mass transfer in mixed convection over a wedge with variable wall temperature and convection in porous media: The entire regime. Int. Comm. Heat Mass Transfer 26, 259–267. [5.7]
Yih, K. A. 2000a Viscous and Joule heating effects on non-Darcy MHD natural convection flow over a permeable sphere in porous media with internal heat generation. Int. Comm. Heat Mass Transfer 27, 591–600. [5.6.1]
Zaturska, M. B. and Banks, W. H. H. 1987 On the spatial stability of free-convection flows in a saturated porous medium. J. Engng. Math. 21, 41–46. [5.1.9.9]
Zhang, J., Subotic, M. and Lai, F. C. 2010 Transient and steady natural convection from a heat sorce embedded in thermally stratified porous layer. Int. J. Them. Sci. 49, 1527–1535. [5.11.1]
Zhao, J. Z. and Chen, T. S. 2002 Inertia effects on non-parallel thermal instability of natural convection flow over horizontal and inclined plates in porous media. Int. J. Heat Mass Transfer 45, 2265–2276. [5.4]
Zhao, J. Z. and Chen, T. S. 2003 Non-Darcy effects on non-parallel thermal instability of horizontal natural convection flow. J. Thermophys. Heat Transfer 17, 150–158. [5.4]
Zueco, J. 2008 Unsteady free-convection-radiation flow over a vertical wall embedded in a porous medium. Comm. Numer. Meth. Engng. 24, 1093–1105. [5.1.9.4]
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Nield, D.A., Bejan, A. (2013). External Natural Convection. In: Convection in Porous Media. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5541-7_5
Download citation
DOI: https://doi.org/10.1007/978-1-4614-5541-7_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-5540-0
Online ISBN: 978-1-4614-5541-7
eBook Packages: EngineeringEngineering (R0)