Abstract
A presentation is made of the basic results on the stability of the convective flow of fluid in a saturated porous medium. The case of convection produced by vertical density gradients in a horizontal layer is treated in detail. Linear stability analysis is presented. The effects of net mass flow, nonlinear basic temperature profiles, anisotropy and inhomogeneity, and double-diffusive and non-Boussinesq effects are incorporated. The energy and perturbation results of nonlinear theory are discussed, together with numerical studies of higher-order transitions. The effects of dispersion and non-Darcy effects are also discussed. Experimental results are surveyed. A briefer survey is made of other stability aspects, including convection produced by vertical density gradients in confined regions (notably rectangular boxes and vertical cylinders), convection produced by horizontal and inclined density gradients (including convection in a sloping layer), and the stability of boundary layers.
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References
Aidun, C.K. (1987) ‘Stability of convection rolls in porous media’, in Bifurcation Phenomena in Thermal Processes and Convection. HTD, 94 and AMD. 89. Amer. Soc. Mech.Engrs., New York.
Aidun, C.K. and Steen, P.H. (1987) ‘Transition of oscillatory convective heat transfer in a fluid-saturated porous medium’, J. Thermophys.Heat Transfer 1, 268–273.
Artem’eva, E.L. and Strogonova, E.V. (1987) ‘Stability of a nonuniformly heated fluid in a porous horizontal layer’, Fluid Dyn. 21, 845–848.
Bau, H.H. and Torrance, K.E. (1981) ‘Onset of convection in a permeable medium between vertical coaxial cylinders’, Phys.Fluids 24, 382–385.
Bau, H.H. and Torrance, K.E. (1982) ‘Low Rayleigh number thermal convection in a vertical cylinder filled with porous materials and heated from below’, ASME J.Heat Transfer 104, 166–172.
Beck, J. L. (1972) ‘Convection in a box of porous material saturated with fluid’, Phys.Fluids 15, 1377–1383.
Bernard, J.J. and Caltagirone, J.P. (1978) ‘Instabilites thermoconvectives en milieu poreux et en gaz rarefies’, in J.C. Legros and J.K. Platten (eds.), Les Instabilites Hydrodynamiques et Convection Libre, Forcée et Mixte. Lecture Notes in Physics, vol.72, pp. 37–53, Springer, Berlin.Bones, S.A. (1987) ‘Natural convection in porous media’, in J. Bear and M.Y. Corapcioglu (eds.), Advances in Transport Phenomena In Porous Media, Martinus Nijhoff, Dordrecht.
Bones, S. and Deltour, A. (1980) ‘Influence des conditions aux limites sur la convection naturelle dans un volume poreux cylindrique’, Int.J.Heat Mass Transfer 23, 765–771.
Borkowska-Pawlak, B. and Kordylewski, W. (1982) ‘Stability of two-dimensional natural convection in a porous layer’, QuartJ.Mech.Appl.Math. 35, 279–290.
Borkowska-Pawlak, B. and Kordylewski, W. (1985) ‘Cell-pattern sensitivity to box configuration in a saturated porous medium’, J.Fluid Mech. 150, 169–181.
Brand, H.R., Hohenberg, P.C. and Steinberg, V. (1983) ‘Amplitude equation near a polycritical point for the convective instability of a binary fluid mixture in a porous medium’, Phys.Rev. A 27, 591–594.
Brand, H. and Steinberg, V. (1983a) ‘Convective instabilities in binary mixtures in a porous medium’, Physica 119A, 327–338.
Brand, H. and Steinberg, V. (1983b) ‘Nonlinear effects in the convective instability of a binary mixture in a porous medium near threshold’, Phys.Lett. 93A, 333–336.
Buretta, R. J. and Berman, A.S. (1976) ‘Convective heat transfer in a liquid saturated porous layer’, ASME J. Appl. Mech. 43, 249–253.
Busse, F.H. (1985) ‘Transition to turbulence in Rayleigh-Bénard convection, in H.L. Swinney and J.P. Gollub (eds.), Hydrodynamic Instabilities and the Transition to Turbulence, 2nd edition, Springer, Berlin, pp. 97–137.
Caltagirone, J. P. (1975) ‘Thermoconvective instabilities in a horizontal porous layer’, J. Fluid Mech. 72, 269–287.
Caltagirone, J. P. (1976a) ‘Stabilité d’une couche poreuse horizontale soumise a des conditions aux limites périodiques’, Int. J. Heat Mass Transfer 19, 815–820.
Caltagirone, J. P. (1976b) ‘Thermoconvective instabilities in a porous medium bounded by two concentric horizontal cylinders’, J. Fluid Mech. 76, 337–362.
Caltagirone. J. P. (1980) ‘Stability of a saturated porous layer subject to a sudden rise in surface temperature: comparison between the linear and energy methods’, Quart. J. Mech. Appl. Math. 33, 47–58.
Caltagirone, J. P. and Bones, S. (1985) ‘Solutions and stability criteria of natural convective flow in an inclined porous layer’, J. Fluid Mech. 155, 267–287.
Caltagirone, J. P. and Fabrie, P. (1989) ‘Natural convection in a porous medium at high Rayleigh numbers. Part 1-Darcy’s model’, Eur. J. Mech. B/Fluids 8, 207–227.
Caltagirone, J. P., Fabrie, P. and Combarnous, M. (1987) ‘De la convection naturelle oscillante en milieu poreux au chaos temporel?’, C.R. Acad. Sci. Paris, Ser. II, 305, 549–553.
Caltagirone, J. P., Meyer, G. and Mojtabi, A. (1981) ‘Structural thermoconvectives tridimensionnelles dans une couche poreuse horizontale’, J. Mecan. 20, 219–232.
Castinel, G., and Combarnous, M.A. (1975) ‘Natural convection in an anisotropic porous layer.’ Rev. Gen. Thermique 168, 937–947. English translation in Int. Chem. Eng. 17, 605-614.
Chakrabarti, A. and Gupta, A.S. (1981) ‘Nonlinear thermohaline convection in a rotating porous medium’, Mech. Res. Comm. 8, 9–22.
Chandrasekhara, B.C. and Hanumanthappa, A.R. (1983) ‘Velocity and temperature distribution in a system consisting of a fluid layer overlying a layer of porous medium’, Proc. Indian Acad. Sci., Math. Sci. 92, 7–18.
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.
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.
Chelgoum, D. E., Weidman, P. D. and Kassoy, D. R. (1987) ‘Effect of slab width on the stability of natural convection in confined saturated porous media’, Phys. Fluids 30, 1941–1947.
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.
Cheng, P. (1978) ‘Heat transfer in geothermal systems’, Advances in Heat Transfer, 14, 1–105.
Chhuon, B. and Caltagirone, J. P. (1979) ‘Stability of a horizontal porous layer with timewise periodic boundary conditions’, ASME J. Heat Transfer 101, 244–248.
Combarnous, M. (1978) ‘Natural convection in porous media and geothermal systems’, Proc. Sixth International Heat Transfer Conference, Toronto, Volume 6, pp.45–59.
Combarnous, M. A. and Bories, S. A. (1975) ‘Hydrothermal convection in saturated porous media’, Advances in Hydroscience, 10, 231–307.
Combarnous, M. A. and Le Fur, B. (1969) ‘Transfert de chaleur par convection naturelle dans une couche poreuse horizontale’, C. R. Acad. Sci. Paris 269B, 1009–1012.
Dandapat, B. S. and Gupta, A. S. (1982) ‘Thermal instability in a porous medium with random vibrations’, Acta Mech. 43, 37–47.
Davidson, M. R. (1986) ‘Natural convection of gas/vapour mixtures in a porous medium’, Int. J. Heat Mass Transfer 29, 1371–1381.
Drazin, P. G. and Reid, W. H. (1981) Hydrodynamic Stability, Cambridge University Press, Cambridge.
Ekholm, T. C., (1983) ‘Studies of convection using a Hele-Shaw cell’, Project Report, School of Engineering, University of Auckland.
Epherre, J. F. (1977) ‘Criterion for the appearance of natural convection in an isotropic porous layer’, Int. J. Chem Engrg 17, 615–616. English translation from Rev.Gen.Thermique 168, 949-950, 1975.
Friedrich, R. (1983) ‘Einfluss der Prandtl-Zahl auf die zellular Konvektion in einem rotierenden, mit Fluid gesättigten porösen Medium’, Zeit. Ang. Math. Mech. 63, T246–T249.
Gasser, R. D. and Kazimi, M. S. (1976) ‘Onset of convection in a porous medium with internal heat generation’, Trans. ASME J. Heat Transfer 98, 49–54.
Gatica, J. E., Viljoen, H. J. and Hlavacek, V. (1987a) ‘Stability analysis of chemical reaction and free convection in porous media’, Int. Comm. Heat Mass Transfer 14, 391–403.
Gatica, J. E., Viljoen, H. J. and Hlavacek, V. (1987b) ‘Thermal instability of nonlinearly stratified flows’, Int. Comm. Heat Mass Transfer 14, 673–686.
Gatica, J. E., Viljoen, H. J. and Hlavacek, V. (1988) ‘Influence of secondary flows on the stability of chemically reacting systems’, AIChE J. 34, 209–222.
Georgiadis, J. G. and Catton, I. (1985) ‘Free convection motion in an infinite vertical porous slot: the non-Darcian regime ‘Int. J. Heat Mass Transfer, 28, 2389–2392.
Georgiadis, J. G. and Catton, I. (1988) ‘Dispersion in cellular thermal convection in porous layers’, Int. J. Heat Mass Transfer 31, 1081–1091.
Gershuni, G. Z., Zhukhovitskii, E. M. and Lyubimov, D.V. (1980) ‘Stability of stationary convective flow of a mixture in a vertical porous layer’, Fluid Dyn. 15, 122–127. English translation from Izv. Akad. Nauk SSSR, Mekh. Zhid. Gaza, no. 1, 150-157, 1980.
Gheorghitza, St.I. (1961) The marginal stability in porous inhomogeneous media. Proc. Camb. Phil. Soc. 57, 871–877.
Gill, A. E. (1969) ‘A proof that convection in a porous vertical slab is stable’, J. Fluid Mech. 35, 545–547.
Gjerde, K.M. and Tyvand, P.A. (1984) ‘Thermal convection in a porous medium with continuous periodic stratification’, Int. J. Heat Mass Transfer 27, 2289–2295.
Gounot, J. and Caltagirone, J. P. (1989) ‘Stabilite et convection naturelle au sein d’une couche poreuse non homogene’, Int. J. Heat Mass Transfer 32, 1131–1140.
Griffiths, R. W. (1981) ‘Layered double-diffusive convection in porous media’, J. Fluid Mech. 102, 221–248.
Hadim, A. and Burmeister, L. C. (1988) ‘Onset of convection in a porous medium with internal heat generation and downward flow. J. Thermophys. Heat Transfer 2, 343–351.
Homsy, G. M. and Sherwood, A. E. (1976) ‘Convective instabilities in porous media with through flow’, AIChE J. 22, 168–174.
Horne, R. N. (1979) ‘Three-dimensional natural convection in a confined porous medium heated from below’, J. Fluid Mech. 92, 751–766.
Horne, R. N. and Caltagirone, J.-P. (1980) ‘On the evolution of thermal disturbances during natural convection in a porous medium’, J. Fluid Mech. 100, 385–395.
Horne, R. N. and O’sullivan, M. J. (1974) ‘Oscillatory convection in a porous medium heated from below’, J. Fluid Mech. 66, 339–352.
Horne, R. N. and O’sullivan, M. J. (1978) ‘Origin of oscillatory convection in a porous medium heated from below’, Phys. Fluids 21, 1260–1264.
Horton, C. W. and Rogers, F. T. (1945) ‘Convection currents in a porous medium.’ J. Appl. Phys. 16, 367–370.
Hsu, C. T. and Cheng, P. (1979) ‘Vortex instability in a buoyancy-induced flow over inclined heated surfaces in porous media’, Trans. ASME J. Heat Transfer 101, 660–665.
Hsu, C. T. and Cheng, P. (1980a) ‘Vortex instability of mixed convection flow in a semi-infinite porous medium bounded by a horizontal surface’, Int. J. Heat Mass Transfer 23, 789–798.
Hsu, C. T. and Cheng, P. (1980b) ‘The onset of longitudinal vortices in mixed convective flow over an inclined surface in a porous medium’, ASME J. Heat Transfer 102, 544–549.
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.
Imhoff, P. T. and Green, T. (1988) ‘Experimental investigation of double-diffusive groundwater fingers’, J. Fluid Mech. 188, 363–382.
Impey, M. D. (1988) Bifurcation in Lapwood Convection, Ph.D. Thesis, University of Bristol.
Impey, M.D., Riley, D.S. and Winters, K.H. (1987) ‘The effect of sidewall imperfections on pattern formation in Lapwood convection’, Bifurcation Phenomena In Thermal Processes and Convection. HTD, 94 and AMD, 89, 99–107. Amer. Soc. Mech. Engrs., New York.
Islam, R. M. and Nandakumar, K. (1986) ‘Multiple solutions for buoyancy-induced flow in saturated porous media for large Péclet numbers’, ASME J. Heat Transfer 108, 866–871.
Islam, R. M. and Nandakumar, K. (1988) ‘Mixed convection heat transfer in porous media in the non-Darcy regime’, Canad. J. Chem. Engrg 66, 68–74.
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.
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.
Jang, J. Y. & Chang, W. J. (1988b) ‘The flow and vortex instability of horizontal natural convection in a porous medium resulting from combined heat and mass buoyancy effects’, Int. J. Heat Mass Transfer 31, 769–777.
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.
Jang, J.-Y. and Tsai, W.-L. (1988) ‘Thermal instability of two horizontal porous layers with a conductive partition’, Int. J. Heat Mass Transfer 31, 993–1003.
Jones, M. C. and Persichetti, J. M. (1986) ‘Convective instability in packed beds with throughflow’, AIChE J. 32, 1555–1557.
Joseph, D. D. (1976) Stability of Fluid Motions I and II, Springer, Berlin.
Joseph, D. D., Nield, D. A. and Papanicolaou, G. (1982) ‘Non-linear equation governing flow in a saturated porous medium’, Water Resour. Res. 18, 1049–1052. Addendum 19, 591.
Jou, J. J. and Liaw, J. S. (1987a) ‘Transient thermal convection in a rotating porous medium confined between two rigid boundaries’, Int. Comm. Heat Mass Transfer 14, 147–153.
Jou, J. J. and Liaw, J. S. (1987b) ‘Thermal convection in a porous medium subject to transient heating and rotation’, Int. J. Heat Mass Transfer 30, 208–211.
Kassoy, D. R. and Cotte, B. (1985) ‘The effects of sidewall heat loss on convection in a saturated porous vertical slab’, J. Fluid Mech. 152, 361–378.
Kassoy, D. R. and Zebib, A. (1975) ‘Variable viscosity effects on the onset of convection in porous media’, Phys. Fluids 18, 1649–1651.
Kassoy, D. R. and Zebib, A. (1978) ‘Convection fluid dynamics in a model of a fault zone in the Earth’s crust’, J. Fluid Mech. 88, 769–792.
Katto, Y. and Masuoka, T. (1967) ‘Criterion for the onset of convective flow in a fluid in a porous medium’, Int. J. Heat Mass Transfer 10, 297–309.
Kaviany, M. (1984a) ‘Thermal convective instabilities in a porous medium’, ASME J. Heat Transfer 106, 137–142.
Kaviany, M (1984b) ‘Onset of thermal convection in a saturated porous medium, experiment and analysis’, Int. J. Heat Mass Transfer 27, 2101–2110.
Khan, A. A. and Zebib, Z. (1981) ‘Double diffusive instability in a vertical layer of porous medium’, ASME J. Heat Transfer 103, 179–181.
Kimura, S., Schubert, G. and Straus, J. M. (1986) ‘Route to chaos in porous-medium thermal convection’, J. Fluid Mech. 166, 305–324.
Kimura, S., Schubert, G. and Straus, J. M. (1987) ‘Instabilities of steady, periodic and quasi-periodic modes of convection in porous media’, ASME J. Heat Transfer 109, 350–355.
Kladias, N. and Prasad, V. (1989) ‘Convective instabilities in horizontal porous layers heated from below: effects of grain size and its properties’ R. K. Shah (ed.), Heat Transfer in Convective Flows, HTD-Vol. 107, ASME, New York, 369–379.
Kolesnikov, A. K. (1978) ‘Convective instability of equilibrium of a chemically active liquid in a horizontal bed of a porous medium’, J. Appl. Mech. Tech. Phys. 19, 114–117. English translation from Zh. Prikl. Mekh. Tekh. Fiz. no.l, 139-143, 1978.
Kolesnikov, A. K. (1979) ‘Concentration-dependent convection in a horizontal porous bed containing a chemically active liquid’, J. Engrg Phys. 36, 97–101.
Kordylewski, W. and Borkowska-Pawlak, B. (1983) ‘Stability of nonlinear thermal convection in a porous medium’, Arch. Mech. 35, 95–106.
Kordylewski, W. and Borkowska-Pawlak, B. &Slany, J. (1987) ‘Stability of three-dimensional natural convection in a porous layer. Arch. Mech. 38, 383–394.
Kulaki, F. A. and Freeman, R. G. (1979) ‘A note on thermal convection in a saturated, heat generating porous layer’, ASME J. Heat Transfer 101, 169–171.
Kumari, S. and Kazarinoff, N. D. (1987) ‘Stability of a free convection density-extremum flow in a porous medium’, Int. J. Heat Mass Transfer 30, 351–361.
Kvernvold, O. and Tyvand, P. A. (1979) ‘Nonlinear thermal convection in anisotropic porous media’, J. Fluid Mech. 90, 609–624.
Kvernvold, O. and Tyvand, P. A. (1980) ‘Dispersion effects on thermal convection in porous media’ J. Fluid Mech. 99, 673–686.
Kwok, L. P. and Chen, C. F. (1987) ‘Stability of thermal convection in a vertical porous layer’, ASME J. Heat Transfer 109, 889–893.
Lapwood, E. R. (1948) ‘Convection of a fluid in a porous medium’, Proc. Camb. Phil. Soc. 44, 508–521.
Lawson, M. L., Yang, W.-J. and Bunditkul, S. (1976) ‘Theory of thermal instability of binary gas mixtures in porous media’, ASME J. Heat Transfer 98, 35–41.
Liubimova, T. P. and Liubimov, D. V. (1981) ‘On convective motions of viscoplastic fluid in a porous medium’, PMM J. Appl. Math. Mech. 45, 208–212. English translation from Prikl. Mat. Mekh. 45, 287-293, 1981.
Lowell, R. P. and Hernandez, H. (1982) ‘Finite amplitude convection in a porous container with fault-like geometry: effect of initial and boundary conditions’, Int. J. Heat Mass Transfer 25, 631–641.
Lowell, R. P. and Shyu, C.-T. (1978) ‘On the onset of convection in a water-saturated porous box: Effect of conducting walls’, Lett. Heat Mass Transfer 5, 371–378.
Lyubimov, D. V. (1975) ‘Convective motions in a porous medium heated from below’, J. Appl. Mech. Tech. Phys. 16, 257–261. English translation from Zh. Prikl. Mekh. Tekh. Fiz. no.2, 131-137, 1975.
Masuoka, T., Katsuhara, T., Nakazono, Y. and Isozaki, S. (1978) ‘Onset of convection and flow patterns in a porous layer of two different media’, Heat Transfer-Japanese Res. 7, 39–52.
McKibbin, R. (1983) ‘Convection in an aquifer above a layer of heated impermeable rock’, N.Z.J. Sci. 26, 49–64.
McKibbin, R. (1985) ‘Thermal convection in layered and anisotropic porous media: a review’, in R. A. Wooding and I. White (eds.), Convective Flows in Porous Media, Dept. Scientific and Industrial Res. Wellington, N.Z., pp. 113–127.
McKibbin, R. (1986a) ‘Thermal convection in a porous layer effects of anisotropy and surface boundary conditions’, Transport Porous Media 1, 271–292.
McKibbin, R. (1986b) ‘Heat transfer in a vertically-layered porous medium heated from below’, Transport Porous Media 1, 361–370.
McKibbin, R. and O’Sullivan, M. J. (1980) ‘Onset of convection in a layered porous medium heated from below’, J. Fluid Mech. 96, 375–393.
McKibbin, R. and O’Sullivan, M. J. (1981) ‘Heat transfer in a layered porous medium heated from below’, J. Fluid Mech. 111, 141–173.
McKibbin, R. and Tyvand, P. A. (1982) ‘Anisotropie modelling of thermal convection in multilayered porous media’, J. Fluid Mech. 118, 315–339.
McKibbin, R. and Tyvand, P. A. (1983) ‘Thermal convection in a porous medium composed of alternating thick and min layers’, Int. J. Heat Mass Transfer 26, 761–780.
McKibbin, R. and Tyvand, P. A. (1984) ‘Thermal convection in a porous medium with horizontal tracks’, Int. J. Heat Mass Transfer 27, 1007–1023.
McKibbin, R., Tyvand, P. A. and Palm, E. (1982) ‘On the recirculation of fluid in a porous layer heated from below’, N.Z.J. Sci. 27, 1–13.
Morland, L. W., Zebib, A. and Kassoy, D. R. (1977) ‘Variable property effects on the onset of convection in an elastic porous matrix’, Phys. Fluids 20, 1255–1259.
Murphy, H. D. (1979) ‘Convective instabilities in vertical fractures and faults’, J. Geophys. Res. 84, 6234–6245.
Murray, B. T. and Chen, C. F. (1989) ‘Double-diffusive convection in a porous medium’, J. Fluid Mech. 201, 147–166.
Nield, D. A. (1968) ‘Onset of thermohaline convection in a porous medium’, Water Resources Res. 4, 553–560.
Nield, D. A. (1975) ‘The onset of transient convective instability’, J. Fluid Mech. 71, 441–454.
Nield, D. A. (1977) ‘Onset of convection in a fluid layer overlying a layer of a porous medium’, J. Fluid Mech. 81, 513–522.
Nield, D. A. (1982) ‘Onset of convection in a porous layer saturated by an ideal gas’, Int. J. Heat Mass Transfer 25, 1605–1606.
Nield, D. A. (1983) ‘The boundary correction for the Rayleigh-Darcy problem: limitations of the Brinkman equation.’ J. Fluid Mech. 128, 37–46.
Nield, D. A. (1987) ‘Convective instability in porous media with throughflow’, AIChE J. 33, 1222–1224.
Nield, D. A. (1990) ‘Convection in a porous medium with inclined temperature gradient’, Accepted for publication in Int. J. Heat Mass Transfer.
Nield, D. A. and Joseph, D. D. (1985) ‘Effects of quadratic drag on convection in a saturated porous medium’, Phys. Fluids 28, 995–997.
Or, A. C. (1989) ‘The effects of temperature-dependent viscosity and the instabilities in convection rolls of a layer of fluid-saturated porous medium’, J. Fluid Mech. 206, 497–515.
Palm, E. and Tyvand, P. (1984) ‘Thermal convection in a rotating porous layer’, J. Appl. Math. Phys.(ZAMP) 35, 122–123.
Palm, E. and Tveitereid, M. (1979) ‘On heat and mass flux through dry snow’, J. Geophys. Res. 84, 745–749.
Palm, E., Weber, J. E. and Kvernvold, O. (1972) ‘On steady convection in a porous medium’, J. Fluid Mech. 54, 153–161.
Patil, P. R. (1982a) ‘Soret driven instability of a reacting fluid in a porous medium’, Israel J. Tech. 19, 193–196.
Patil, P. R. (1982b) ‘Convection in a porous medium with nonlinear density effects’, Lett. Heat Mass Transfer 9, 131–140.
Patil, P. R., Parvathy, C. P. and Venkatakrishnan, K. S. (1989) Thermohaline instability in a rotating anisotropic porous medium. Appl. Sci. Res. 46, 73–88.
Patil, P. R. and Rudraiah, N. (1973) ‘Stability of hydromagnetic thermoconvective flow through porous medium’, Trans. ASME J. Appl. Mech. 40, 879–884.
Patil, P. R. and Rudraiah, N. (1980) ‘Linear convective stability and thermal diffusion of a horizontal quiescent layer of a two component fluid in a porous medium’, Int. J. Engrg Sci. 18, 1055–1059.
Patil, P. R. and Vaidyanathan, G. (1981) ‘Effect of variable viscosity on the setting up of convection currents in a porous medium’, Int. J. Engrg Sci. 19, 421–426.
Patil, P. R. and Vaidyanathan, G. (1982) ‘Effect of variable viscosity on thermohaline convection in a porous medium’, J. Hydrol. 57, 147–161.
Patil, P. R. and Vaidyanathan, G. (1983) ‘On setting up of convection currents in a routing porous medium under the influence of variable viscosity’, Int. J. Engrg Sci. 21, 123–130.
Pillatsis, G., Taslim, M. E. and Narusawa, U. (1987) ‘Thermal instability of a fluid-saturated porous medium bounded by thin layers’, ASME J. Heat Transfer 109, 677–682.
Poulikakos, D. (1985) ‘Onset of convection in a horizontal porous layer saturated with cold water’, Int. J. Heat Mass Transfer 28, 1899–1905.
Poulikakos, D. (1986) ‘Double diffusive convection in a horizontally sparsely packed porous layer’, Int. Comm. Heat Mass Transfer 13, 587–598.
Poulikakos, D. (1987) ‘Thermal instability in a horizontal fluid layer superposed on a heat-generating porous bed’, Num. Heat Transfer 12, 83–100.
Prabhamani, P. R. and Rudraiah, N. (1974) ‘Thermal convection of a conducting fluid in a porous medium’, Israel. J. Tech. 12, 89–98.
Prats, M. (1966) ‘The effect of horizontal fluid flow on thermally induced convection currents in porous media’, J. Geophys. Res. 71, 4835–4838.
Quintard, M. and Prouvost, L. (1982) ‘Instabilites de zones de diffusion thermique instationnaires en milieu poreux’, Int. J. Heat Mass Transfer 25, 37–44.
Rana, R., Horne, R. N., and Cheng, P. (1979) ‘Natural convection in a multi-layered geothermal reservoir’, ASME J. Heat Transfer 101, 411–416
Rees, D. A. S. (1988) ‘The stability of Prandtl-Darcy convection in a porous layer’, Int. J. Heat Mass Transfer, 31, 1529–1534.
Rees, D. A. S. and Riley, D. S. (1986) ‘Free convection in an undulating saturated porous layer: resonant wavelength exitation. J. Fluid Mech. 166, 503–530.
Rees, D. A. S. and Riley, D. S. (1989a) ‘The effects of boundary imperfections on convection in a saturated porous layer non-resonant wavelength excitation’, Proc. Roy. Soc. Lond. A 421, 303–339.
Rees, D. A. S. and Riley, D. S. (1989b) ‘Effects of boundary imperfections on convection in a saturated porous layer near resonant wavelength excitation’, J. Fluid Mech. 199, 133–154.
Riahi, N. (1983) ‘Nonlinear convection in a porous layer with finite conducting boundaries’, J. Fluid Mech. 129, 153–171.
Riahi, N. (1984) ‘Non-linear convection in a porous medium with internal heat sources’, lnt. J. Non-Linear Mech. 10, 469–478.
Richard, J.-P. and Gounot, J. (1981) ‘Critere d’apparition de la convection naturelle dans des couches poreuses stratifiees’, Int. J. Heat Mass Transfer 24, 1325–1334.
Riley, D. S. and Winters, K. H. (1989) ‘Modal exchange mechanisms in Lapwood convection’, J. Fluid Mech. 204, 325–358.
Rubin, H. (1977) ‘Thermal convection in a cavernous aquifer’, Water Resour. Res. 13, 34–40.
Rubin, H. (1981) ‘Onset of thermohaline convection in heterogeneous porous media’, Israel J. Tech. 19, 110–117.
Rubin, H. (1982a) ‘Thermohaline convection in a nonhomogeneous aquifer’, J. Hydrol. 57, 307–320.
Rubin, H. (1982b) ‘Application of the aquifer’s average characteristics for determining the onset of thermohaline convection in a heterogeneous aquifer’, J. Hydrol. 57, 321–336.
Rubin, H. and Roth, C. (1978) ‘Instability of horizontal thermohaline flow in a porous medium layer’, Israel J. Tech. 16, 216–223.
Rubin, H. and Rom, C. (1979) ‘On the growth of instabilities in groundwater due to temperature and salinity gradients’, Adv. Water Resour. 2, 69–76.
Rubin, H. and Roth, C. (1983) ‘Thermohaline convection in flowing groundwater’. Adv. Water Resour. 6, 146–156.
Rudraiah, N. (1972) ‘Universal stability of hydromagnetic convective flows in a porous medium’, Indian J. Pure Appl. Math. 3, 681–694.
Rudraiah, N. (1984) ‘Linear and non-linear magnetoconvection in a porous medium’, Proc. Indian Acad. Sci.(Math. Sci.) 93, 117–135.
Rudraiah, N. and Prabhamani, P. R. (1974) ‘Thermal diffusion and convective instability of two component fluid in a porous medium’, Heat Transfer 1974, vol.V. pp. 79–82. Proc. 5th Int. Heat Transfer Conf., Tokyo. Japan Soc. Mech. Engrs and Soc. Chem. Engrs Japan.
Rudraiah, N., Shivakumara, I. S. and Friedrich, R. (1986) ‘The effect of rotation on linear and non-linear double-diffusive convection in a sparsely packed, porous medium’, Int. J. Heat Mass Transfer 29, 1301–1317.
Rudraiah, N. and Srimani, P. K. (1980) ‘Finite-amplitude cellular convection in a fluid-saturated porous layer’, Proc. Roy. Soc. A 373, 199–222.
Rudraiah, N., Srimani, P. K. and Friedrich, R. (1982) ‘Finite amplitude convection in a two-component fluid saturated porous layer’, Int. J. Heat Mass Transfer 25, 715–722.
Rudraiah, N., Veerappa, B. and Balachandra Rao, S. (1980) ‘Effects of nonuniform gradient and adiabatic boundaries on convection in porous media’, ASME J. Heat Transfer 102, 254–260.
Rudraiah, N., Veerappa, B. and Balachandra Rao, S. (1982) ‘Convection in a fluid-saturated porous layer with non-uniform temperature gradient’, Int. J. Heat Mass Transfer 25, 1147–1156.
Rudraiah, N. and Vortmeyer, D. (1978) ‘Stability of finite-amplitude and overstable convection of a conducting fluid through fixed porous bed’, Warme Stoff. 11, 241–254.
Rudraiah, N. and Vortmeyer, D. (1982) ‘The influence of permeability and of a third diffusing component upon the onset of convection in a porous medium’, Int. J. Heat Mass Transfer 25, 457–464.
Schubert, G. and Straus, J. M. (1977) ‘Two phase convection in a porous medium’, J. Geophys. Res. 82, 3411–3421.
Schubert, G. and Straus, J. M. (1979) ‘Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers’, J. Fluid Mech. 94, 25–38.
Schubert, G. and Straus, J. M. (1980) ‘Gravitational stability of water over steam in vapor-dominated geothermal systems’, J. Geophys. Res. 85, 6505–6512.
Schubert, G. and Straus, J. M. (1982) ‘Transitions in time-dependent thermal convection in fluid-saturated porous media’, J. Fluid Mech. 12, 1301–313.
Schlüter, A., Lortz, D. and Busse, F. H. (1965) ‘On the stability of steady finite amplitude cellular convection’, J. Fluid Mech. 23, 129–144.
Selimos, B. and Poulikakos, D. (1985) ‘On double diffusion in a Brinkman heat generating porous layer’, Int. Comm. Heat Mass Transfer 12, 149–158.
Sen, M., Vasseur, P. and Robillard, L. (1987) ‘Multiple steady states for unicellular natural convection in an inclined porous layer’, Int. J. Heat Mass Transfer 30, 2097–2113.
Sen, M., Vasseur, P. and Robillard, L. (1988) ‘Parallel flow convection in a tilted two-dimensional porous layer heated from all sides’, Phys. Fluids 31, 3480–3487.
Sharma, R.C. (1977) ‘Thermal instability of fluids with Hall currents through porous medium’, Middle East Tech. Univ. J. Pure Appl. Sci. 10, 231–239.
Sharma, R.C. (1978) ‘Effect of compressibility on thermal instability of fluids through porous medium’, Middle East Tech. Univ. J. Pure Appl. Sci. 11, 101–110.
Sharma, R.C. and Rani, N. (1987) ‘Effect of suspended particles on thermosolutal convection in porous medium’, Indian J. Pure Appl. Math. 18, 178–185.
Sharma, R.C. and Sharma, K.N. (1977) ‘Thermal instability of a rotating Maxwell fluid through porous medium’, Middle East Tech. Univ. J. Pure Appl. Sci. 10, 223–230.
Sharma, R.C. and Sharma, K.N. (1980) ‘Magneto-thermohaline convection through porous medium’, Acta Phys. Acad. Sci. Hung. 48, 269–279.
Sharma, R.C. and Sharma, K.N. (1982) ‘Thermal instability of fluids through a porous medium in the presence of suspended particles, rotation and solute gradient’, J. Math. Phys. Sci. 16, 167–181.
Sharma, R.C. and Singh, H. (1980) ‘Thermal-convective instability through porous medium’, Astrophys. Space Sci. 68, 3–9.
Somerton, C.W. and Catton, I. (1982) ‘On the thermal instability of superposed porous and fluid layers’, ASME J. Heat Transfer 104, 160–165.
Somerton, C.W. and Goff, J.D. (1985) ‘Experiments on natural convection in a two layer porous media with varying permeabilities’, in Heat Transfer in Porous Media and Particulate Flows, HTD Volume 46, ASME, New York.
Steen, P.H. (1983) ‘Pattern selection for finite-amplitude convection states in boxes of porous media’, J. Fluid Mech. 136, 219–241.
Steen, P.H. (1986) ‘Container geometry and the transition to unsteady Bénard convection in porous media’, Phys. Fluids 29, 925–933.
Steen, P.H. and Aidun, C.K. (1988) ‘Time-periodic convection in porous media’, J. Fluid Mech. 196, 263–290.
Steinberg, V. and Brand, H. (1983) ‘Convective instabilities of binary mixtures with fast chemical reaction in a porous medium’, J. Chem. Phys. 78, 2655–2660.
Straughan, B. (1988) ‘A nonlinear analysis of convection in a porous vertical slab’, Geophys. Astrophys. Fluid Dyn. 42, 269–276.
Straus, J.M. (1974) ‘Large amplitude convection in porous media’, J. Fluid Mech. 64, 51–63.
Straus, J.M. and Schubert, G. (1977) ‘Thermal convection of water in a porous medium: Effects of temperature-and pressure-dependent thermodynamic and transport processes’, J.Geophys.Res. 82, 325–333.
Straus, J.M. and Schubert, G. (1979) ‘Three-dimensional convection in a cubic box of fluid-saturated porous material’, J.Fluid Mech. 91, 155–165.
Straus, J.M. and Schubert, G. (1981) ‘Modes of finite-amplitude three-dimensional convection in rectangular boxes of fluid-saturated porous material’, J.Fluid Mech. 103, 23–32.
Taslim, M.E. and Narusawa, U. (1986) ‘Binary fluid convection and double-diffusive convection in a porous medium’ ASME J.Heat Transfer 108, 221–224.
Taslim, M.E. and Narusawa, U. (1989) ‘Thermal instability of horizontally superposed porous and fluid layers’, ASME J.Heat Transfer 111, 357–362.
Tewari, P.K. and Torrance, K.E. (1981) ‘Onset of convection in a box of fluid-saturated porous material with a permeable top’, Phys.Fluids 24, 981–983.
Tveitereid, M. (1977) ‘Thermal convection in a horizontal porous layer with internal heat sources’, Int.J.Heat Mass Transfer 20, 1045–1050.
Tyvand, P.A. (1977) ‘Heat dispersion effect on thermal convection in anisotropic porous media’, J.Hydrol. 34, 335–342.
Tyvand, P.A. (1980) ‘Thermohaline instability in anisotropic porous media’, Water Resour.Res. 16, 325–330.
Tyvand, P.A. (1981) ‘Influence of heat dispersion on steady convection in anisotropic porous media’, J.Hydrol. 52, 13–23.
Vasseur, P., Wang, C.H. and Sen, M. (1989) ‘Thermal instability and natural convection in a fluid layer over a porous substrate’, Warme Stoff. 24, 337–348.
Vincourt, M.C. (1989a) ‘Competition between two directions of connective rolls in a horizontal porous layer, non-uniformly heated’, Mechanics 16, 19–24.
Vincourt, M.C. (1989b) ‘Influence of a heterogeneity on the selection of convective patterns in a porous layer’, Int.J.Engrg.Sci. 27, 377–392.
Vortmeyer, D., Rudraiah, N. and Sasikumar, T.P. (1989) ‘Effect of radiative transfer on the onset of convection in a porous medium’, Int.J.Heat Mass Transfer 32, 873–879.
Walker, K. and Homsy, G.M. (1977) ‘A note on convective instabilities in Boussinesq fluids and porous media’, ASME J. Heat Transfer 99, 338–339.
Wang, M., Kassoy, D.R. and Weidman, P.D. (1987) ‘Onset of convection in a vertical slab of saturated porous media between two impermeable conducting blocks’, Int.J.Heat Mass Transfer 30, 1331–1314.
Weber, J.E. (1974) ‘Convection in a porous medium with horizontal and vertical temperature gradients’, Int.J.Heat Mass Transfer 17, 241–248.
Weber, J.E. (1975) ‘Thermal convection in a tilted porous layer’, Int.J.Heat Mass Transfer 18, 474–475.
Weidman, P.D. and Kassoy, D.R. (1986) ‘Influence of side wall heat transfer on convection in a confined saturated porous medium’, Phys.Fluids 29, 349–355.
Wesfreid, J.E. and Borgis, D. (1984) ‘Oscillations monopériodiques dans la convection en milieu poreux’, C.R.Acad.Sci.Paris, II, 298, 775–778.
Westbrook, D.R. (1969) ‘Stability of convective flow in a porous medium’, Phys.Fluids 12, 1547–1551.
Wolanski, E.J. (1973) ‘Convection in a vertical porous slab’, Phys.Fluids 16, 2014–2016.
Wolanski, E.J. (1974) ‘Convection in a horizontal porous gap’, Phys.Fluids 17, 654–656.
Wooding, R.A. (1959) ‘The stability of a viscous fluid in a vertical tube containing porous material’, Proc.Roy.Soc. A 252, 120–134.
Wooding, R.A. (1960a) ‘Instability of a viscous liquid of variable density in a vertical Hele-Shaw cell’, J.Fluid Mech. 7, 501–515.
Wooding, R.A. (1960b) ‘Rayleigh instability of a thermal boundary layer in flow through a porous medium’, J.Fluid Mech. 9, 183–192.
Wooding, R.A. (1978) ‘Large-scale geothermal field parameters and convection theory’, N.Z.J.Sci. 21, 219–228.
Wu, K.S., Cheng, K.C. and Craggs, A. (1979) ‘Convective instabilities in porous media with maximum density and throughflow effects by finite-difference and finite-element methods’, Num.Heat Transfer 2, 303–318.
Yen, Y.C. (1974) ‘Effects of density inversion on free convective heat transfer in porous layer heated from below’, Int.J.Heat Mass Transfer 17, 1349–1356.
Zebib, A. (1978) ‘Onset of natural convection in a cylinder of water saturated porous media’, Phys.Fluids 21, 699–700.
Zebib, A. and Kassoy, D.R. (1977) ‘Onset of natural convection in a box of water-saturated porous media with large temperature variation’, Phys.Fluids 20, 4–9.
Zebib, A. and Kassoy, D.R. (1978) ‘Three-dimensional natural convection motion in a confined porous medium’, Phys.Fluids 21, 1–3.
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Nield, D.A. (1991). The Stability Of Convective Flows In Porous Media. In: Kakaç, S., Kilkiş, B., Kulacki, F.A., Arinç, F. (eds) Convective Heat and Mass Transfer in Porous Media. NATO ASI Series, vol 196. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3220-6_4
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