Advertisement

Introduction

  • De-Yi ShangEmail author
  • Liang-Cai Zhong
Chapter
Part of the Heat and Mass Transfer book series (HMT)

Abstract

This chapter introduces recent advanced study on laminar mixed convection of liquid with focusing on its hydrodynamics and heat transfer. Taking water laminar mixed convection as an example enables researchers to targeted study of this book. On this basis, three activities are performed in order for enhancement of the theoretical and practical value of the study. First, for simplification of the study, the governing partial differential equations are equivalently transformed into the ordinary differential equations by using an innovative similarity transformation model of velocity field. Based on such simplification, the study can focus on successive even difficult and complicated issues of heat transfer. Second, coupled effect of variable physical properties is considered. It is an assurance that the systems of numerical solutions have their practical value. Third, based on the theoretical equations and the systems of rigorous numerical solutions, the optimal formalized equations of Nusselt number are created for convenient and reliable application of heat transfer, in view of that so far, there is still lack of such reliable theoretical achievements. These theoretical achievements with the optimal formalized equations are base on the systems of reliable numerical solutions with a better consideration of variable physical properties, they have solidly theoretical and practical value for heat transfer application.

Keywords

Mixed convection Heat transfer Innovative similarity transformation Mixed convection parameter Positive flow Variable physical properties Theoretical and practical value 

References

  1. 1.
    Gebhart, B., Jaluria, Y., Mahajan, R.L., Sammakia, B.: Buoyancy-induced Flows and Transport. Hemisphere, New York (1988)Google Scholar
  2. 2.
    Bejan, A.: Convective Heat Transfer. Wiley Inter Science, New York (1994)Google Scholar
  3. 3.
    Pop, I., Ingham, D.B.: Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media. Elsevier UK (2001)Google Scholar
  4. 4.
    Sparrow, E.M., Eichhorn, R., Gregg, J.L.: Combined forced and free convection in a boundary layer flow. Phys. Fluids 2, 319–328 (1959)Google Scholar
  5. 5.
    Szewcyk, A.A.: Combined forced and free convection laminar flow. J. Heat Transf., Trans. ASME, Ser. C 86(4), 501–507 (1964)Google Scholar
  6. 6.
    Metais, B., Eckert, E.R.G.: Forced, mixed, and free convection regimes. J. Heat Transf. 86, 295–296 (1964)CrossRefGoogle Scholar
  7. 7.
    Acrivos, A.: On the combined effect of forced and free convection heat transfer in laminar boundary layer flows. Chem. Eng. Sci. 21(4), 343–352 (1966)CrossRefGoogle Scholar
  8. 8.
    Acrivos, A.: Combined laminar free and forced convection heat transfer in external flows. AIChE J. 4, 285–289 (1958)CrossRefGoogle Scholar
  9. 9.
    Wilks, G.: Combined forced and free convection flow on vertical surfaces. Int. J. Heat Mass Transf. 16, 1958–1966 (1973)CrossRefzbMATHGoogle Scholar
  10. 10.
    Lloyd, J.R., Sparrow, E.M.: Combined forced and free convection flow on vertical surfaces. Int. J. Heat Mass Transf. 13(2), 434–438 (1970)CrossRefGoogle Scholar
  11. 11.
    Robertson, G.E., Seinfield, J.H., Leal, L.G.: Combined forced and free convection flow past horizontal plate. AIChE J. 19, 998–1008 (1972)CrossRefGoogle Scholar
  12. 12.
    Oosthuizen, P.H., Hart, R.: A numerical study of laminar combined convection flow over flat plates. J. Heat Transf. 95, 60–63 (1973)Google Scholar
  13. 13.
    Wilks, G.: Combined forced and free convection flow on vertical surfaces. Int. J. Heat Mass Transf. 16(10), 1958–1964 (1973)CrossRefzbMATHGoogle Scholar
  14. 14.
    Mucoglu, A., Chen, T.S.: Mixed convection on inclined surface. J. Heat Transf. 101, 422–426 (1979)CrossRefGoogle Scholar
  15. 15.
    Chen, T.S., Yuh, C.F., Moutsoglou, A.: Combined heat and mass transfer in mixed convection along vertical and inclined plates. Int. J. Heat Mass Transf. 23(4), 527–537 (1980)ADSCrossRefzbMATHGoogle Scholar
  16. 16.
    Tsuruno, S., Iguchi, I.: Prediction of combined free and forced convective heat transfer along a vertical plate with blowing. ASME J. Heat Transf. 102, 168–170 (1980)CrossRefGoogle Scholar
  17. 17.
    Raju, M.S., Liu, X.R., Law, C.K.: A formulation of combined forced and free convection past horizontal and vertical surfaces. Int. J. Heat Mass Transf. 27(12), 2215–2224 (1984)CrossRefzbMATHGoogle Scholar
  18. 18.
    Afzal, N., Hussain, T.: Mixed convection over a horizontal plate. J. Heat Transf. 106(1), 240–241 (1984)CrossRefGoogle Scholar
  19. 19.
    Chen, T.S., Armaly, B.F., Ramachandran, N.: Correlations for laminar mixed convection flows on vertical, inclined, and horizontal flat plates. ASME J. Heat Transf. 108, 835–840 (1986)CrossRefGoogle Scholar
  20. 20.
    Yao, L.S.: Two-dimensional mixed convection along a flat plate. ASME J. Heat Transf. 109, 440–445 (1987)CrossRefGoogle Scholar
  21. 21.
    Wickern, G.: Mixed convection from an arbitrarily inclined semi-infinite flat plate-I. The influence of the inclination angle. Int. J. Heat Mass Transf. 34, 1935–1945 (1991)ADSCrossRefzbMATHGoogle Scholar
  22. 22.
    Wickern, G.: Mixed convection from an arbitrarily inclined semi-infinite flat plate-II. The influence of the Prandtl number. Int. J. Heat Mass Transf. 34, 1947–1957 (1991)CrossRefzbMATHGoogle Scholar
  23. 23.
    Gorla, R.S.R.: Mixed convection in a micropolar fluid along a vertical surface with uniform heat flux. Int. J. Eng. Sci. 30(3), 349–358 (1992)CrossRefGoogle Scholar
  24. 24.
    Kafoussias, N.G., Williams, E.W.: The effect of temperature-dependent viscosity on free-forced convective laminar boundary layer flow past a vertical isothermal flat plate. Acta Mech. 110(1–4), 123–137 (1995)CrossRefzbMATHGoogle Scholar
  25. 25.
    Lin, H.T., Hoh, H.L.: Mixed convection from an isothermal vertical flat plate moving in parallel or reversely to a free stream. Heat Mass Transf. 32(6), 441–445 (1997)ADSCrossRefGoogle Scholar
  26. 26.
    Hossain, M.A., Munir, M.S.: Mixed convection flow from a vertical flat plate with temperature dependent viscosity. Int. J. Therm. Sci. 39, 173–183 (2000)CrossRefGoogle Scholar
  27. 27.
    Merkin, J.H., Pop, I.: Mixed convection along a vertical surface: similarity solutions for uniform flow. Fluid Dyn. Res. 30, 233–250 (2002)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Steinrück, H.: About the physical relevance of similarity solutions of the boundary-layer flow equations describing mixed convection flow along a vertical plate. Fluid Dyn. Res. 32, 1–13 (2003)Google Scholar
  29. 29.
    Ali, M.E.: The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface. Int. J. Therm. Sci. 45, 60–69 (2006)CrossRefGoogle Scholar
  30. 30.
    Ali, M., Al-Yousef, F.: Laminar mixed convection from a continuously moving vertical surface with suction or injection. Heat Mass Transf. 33(4), 301–306 (1998)ADSCrossRefGoogle Scholar
  31. 31.
    Chen, C.H.: Mixed convection cooling of a heated, continuously stretching surface. Heat Mass Transf. 36(1), 79–86 (2000). View at Publisher · View at Google ScholarGoogle Scholar
  32. 32.
    Al-Sanea, S.A.: Mixed convection heat transfer along a continuously moving heated vertical plate with suction or injection. Int. J. Heat Mass Transf. 47, 1445–1465 (2004)CrossRefzbMATHGoogle Scholar
  33. 33.
    Chen, C.H.: Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat Mass Transf. 33(5/6), 471–476 (1998) (continue moving surface)Google Scholar
  34. 34.
    Hieber, C., Gebhart, B.: Mixed convection from a sphere at small Reynolds and Grashof numbers. J. Fluid Mech. 38(1), 137–159 (1969)ADSCrossRefzbMATHGoogle Scholar
  35. 35.
    Mucoglu, A., Chen, T.: Mixed convection about a sphere with uniform surface heat flux. J. Heat Transf. 100, 542–544 (1978)CrossRefGoogle Scholar
  36. 36.
    Dudek, D.R., Fletcher, T.H., Longwell, J.P., Sarofim, A.F.: Natural convection induced drag forces on spheres at low Grashof numbers: comparison of theory with experiment. Int. J. Heat Mass Transf. 31(4), 863–873 (1988)CrossRefGoogle Scholar
  37. 37.
    Tang, L., Johnson, A.T.: Flow visualization of mixed convection about a sphere. Int. Commun. Heat Mass Transf. 17(1), 67–77 (1990)CrossRefGoogle Scholar
  38. 38.
    Koizumi, H., Umemura, Y., Hando, S., Suzuki, K.: Heat transfer performance and the transition to chaos of mixed convection around an isothermally heated sphere placed in a uniform, downwardly directed flow. Int. J. Heat Mass Transf. 53(13), 2602–2614 (2010)CrossRefzbMATHGoogle Scholar
  39. 39.
    Nazar, R., Amin, N., Pop, I.: On the mixed convection boundary-layer flow about a solid sphere with constant surface temperature. Arab. J. Sci. Eng. 27(2), 117–135 (2002)Google Scholar
  40. 40.
    Nazar, R., Amin, N., Pop, I.: Mixed convection boundary layer flow about an isothermal sphere in a micropolar fluid. Int. J. Therm. Sci. 42(3), 283–293 (2003)Google Scholar
  41. 41.
    Bhattacharyya, S., Singh, A.: Mixed convection from an isolated spherical particle. Int. J. Heat Mass Transf. 51(5), 1034–1048 (2008)CrossRefzbMATHGoogle Scholar
  42. 42.
    Gebhart, B., Pera, L.: Mixed convection from long horizontal cylinders. J. Fluid Mech. 45, 49–64 (1970)ADSCrossRefGoogle Scholar
  43. 43.
    Aman, F., Ishak, A.: Mixed convection boundary layer flow towards a vertical plate with a convective surface boundary condition. Math. Probl. Eng. 2012 (2012)Google Scholar
  44. 44.
    Ramachandran, N., Chen, T.S., Armaly, B.F.: Mixed convection in stagnation flows adjacent to vertical surfaces. J. Heat Transf. 110(2), 373–377 (1988)CrossRefGoogle Scholar
  45. 45.
    Ishak, A., Nazar, R., Pop, I.: Dual solutions in mixed convection boundary-layer flow with suction or injection. IMA J. Appl. Math. 72(4), 451–463 (2007)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Watanabe, T.: Forced and free mixed convection boundary layer flow with uniform suction or injection on a vertical flat plate. Acta Mech. 89, 123–132 (1991)CrossRefzbMATHGoogle Scholar
  47. 47.
    Ishak, A., Merkin, J.H., Nazar, R., Pop, I.: Mixed convection boundary layer flow over a permeable vertical surface with prescribed wall heat flux. Z. Angew. Math. Phys. 59(1), 100–123 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Bachok, N., Ishak, A., Pop, I.: Mixed convection boundary layer flow over a permeable vertical flat plate embedded in an anisotropic porous medium. Math. Probl. Eng. 2010, Article ID 659023, 12 p. (2010)Google Scholar
  49. 49.
    Rana, P., Bhargava, R.: Numerical study of heat transfer enhancement in mixed convection flow along a vertical plate with heat source/sink utilizing nanofluids. Commun. Nonlinear Sci. Numer. Simul. 16, 4318–4334 (2011)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Aydin, O., Kaya, A.: Mixed convection of a viscous dissipating fluid about a vertical flat plate. Appl. Math. Model. 31, 843–853 (2007)CrossRefzbMATHGoogle Scholar
  51. 51.
    Partha, M.K., Murthy, P.V.S.N., Rajasekhar, G.P.: Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface. Heat Mass Transf. 41(4), 360–366 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    Gorla, R.S.R., Lin, P.P., Yang, A.J.: Asymptotic boundary layer solutions for mixed convection from a vertical surface in a micropolar fluid. Int. J. Eng. Sci. 28(6), 525–533 (1990)CrossRefzbMATHGoogle Scholar
  53. 53.
    Lok, Y.Y., Amin, N., Campean, D., Pop, I.: Steady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface. Int. J. Numer. Meth. Heat Fluid Flow 15(7), 654–670 (2005)CrossRefGoogle Scholar
  54. 54.
    Hossain, M.A., Ahmed, M.U.: MHD forced and free convection boundary layer flow near the leading edge. Int. J. Heat Mass Transf. 33(3), 571–575 (1990)CrossRefGoogle Scholar
  55. 55.
    Merkin, J.H., Mahmood, T.: Mixed convection boundary layer similarity solution: prescribed wall heat flux. ZAMP 40, 61–68 (1989)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Sabbagh, J.A., Aziz, A., EI-Ariny, A.S., Hamad, G.: Combined free and forced convection in inclined circular tubes. J. Heat Transf. 98, 322–324 (1976)Google Scholar
  57. 57.
    Lee, K.T., Yan, W.M.: Mixed convection heat transfer in horizontal ducts with wall temperature effect. Int. J. Heat Mass Transf. 41, 411–424 (1998)CrossRefzbMATHGoogle Scholar
  58. 58.
    Barletta, A.: Analysis of combined forced and free convection in a vertical channel with viscous dissipation and isothermal-isoflux boundary conditions. ASME J. Heat Transf. 121, 349–356 (1999)CrossRefGoogle Scholar
  59. 59.
    Yuge, T.: Experiments on heat transfer from spheres including combined natural and forced convection. J. Heat Transf. 82, 214–220 (1960)CrossRefGoogle Scholar
  60. 60.
    Oosthuizen, P.H., Bassey, M.: An experimental study of combined forced and free convection heat transfer from flat plates to air at low Renolds number. J. Heat Transf. 95, 120–121 (1973)CrossRefGoogle Scholar
  61. 61.
    Marcos, S.M., Bergles, A.E.: Experimental investigation of combined forced and free laminar convection in horizontal tubes. J. Heat Transf. 97, 212–219 (1975)CrossRefGoogle Scholar
  62. 62.
    Ramachandran, N., Armaly, B.F., Chen, T.S.: Measurements and predictions of laminar mixed convection flow adjacent to a vertical surface. J. Heat Transf. 107, 636–641 (1985)CrossRefGoogle Scholar
  63. 63.
    Ramachandran, N., Armaly, B.F., Chen, T.S.: Measurements of laminar mixed convection flow adjacent to an inclined surface. J. Heat Transf. 109, 146–151 (1987)CrossRefGoogle Scholar
  64. 64.
    Mograbi, E., Ziskind, G., Katoshevski, D., Bar-Ziv, E.: Experimental study of the forces associated with mixed convection from a heated sphere at small Reynolds and Grashof numbers. Part II: assisting and opposing flows. Int. J. Heat Mass Transf. 45(12), 2423–2430 (2002)CrossRefGoogle Scholar
  65. 65.
    Ziskind, G., Zhao, B., Katoshevski, D., Bar-Ziv, E.: Experimental study of the forces associated with mixed convection from a heated sphere at small Reynolds and Grashof numbers. Part I: cross-flow. Int. J. Heat Mass Transf. 44(23), 4381–4389 (2001)CrossRefGoogle Scholar
  66. 66.
    Cheng, P.: Combined free and forced boundary layer flows about inclined surfaces in a porous medium. Int. J. Heat Mass Transf. 20, 807–814 (1977)CrossRefzbMATHGoogle Scholar
  67. 67.
    Merkin, J.H.: Mixed convection boundary layer flow on a vertical surface in a saturated porous medium. J. Eng. Math. 14(4), 301–313 (1980)Google Scholar
  68. 68.
    Hsieh, J.C., Chen, T.S., Armaly, B.F.: Non-similarity solutions for mixed convection from vertical surfaces in porous media: variable surface temperature or heat flux. Int. J. Heat Mass Transf. 36, 1485–1493 (1993)CrossRefzbMATHGoogle Scholar
  69. 69.
    Chen, C.H.: Non-Darcy mixed convection over a vertical flat plate in porous media with variable wall heat flux. Int. Commun. Heat Mass Transf. 24, 427–438 (1997)CrossRefGoogle Scholar
  70. 70.
    Harris, S.D., Ingham, D.B., Pop, I.: Unsteady mixed convection boundary layer flow on a vertical surface in a porous medium. Int. J. Heat Mass Transf. 42, 357–372 (1998)CrossRefzbMATHGoogle Scholar
  71. 71.
    Harris, S.D., Ingham, D.B., Pop, I.: Unsteady mixed convection boundary-layer flow on a vertical surface in a porous medium. Int. J. Heat Mass Transf. 42, 357–372 (1999)CrossRefzbMATHGoogle Scholar
  72. 72.
    Harris, S.D., Ingham, D.B., Pop, I.: Unsteady mixed convection boundary layer flow on a vertical surface in a porous medium. Int. J. Heat Mass Transf. 42(2), 357–372 (1999)CrossRefzbMATHGoogle Scholar
  73. 73.
    Kumari, M., Takhar, H.S., Nath, G.: Mixed convection flow over a vertical wedge embedded in a highly porous medium. Heat Mass Transf. 37, 139–146 (2001)ADSCrossRefGoogle Scholar
  74. 74.
    Aly, E.H., Elliot, L., Ingham, D.B.: Mixed Convection boundary-layer flow over a Vertical surface embedded in a porous medium. Eur. J. Mech. B/Fluids 22, 529–543 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  75. 75.
    Alam, M.S., Rahman, M., Samad, M.A.: Numerical study of the Combined free-forced convection and mass transfer flow past a vertical porous plate in a porous medium with heat generation and thermal diffusion. Nonlinear Anal. Model. Contr. 11(4), 331–343 (2006)zbMATHGoogle Scholar
  76. 76.
    Chin, K.E., Nazar, R., Arifin, N.M., Pop, I.: Effect of variable viscosity on mixed convection boundary layer flow over a vertical surface embedded in a porous medium. Int. Commun. Heat Mass Transf. 34, 464–473 (2007)CrossRefGoogle Scholar
  77. 77.
    Ishak, A., Nazar, R., Pop, I.: Dual solutions in mixed convection flow near a stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transf. 51(5–6), 1150–1155 (2008). View at Publisher · View at Google Scholar · View at ScopusGoogle Scholar
  78. 78.
    Ishak, A., Nazar, R., Arifin, N.M., Pop, I.: Dual solutions in mixed convection flow near a stagnation point on a vertical porous plate. Int. J. Therm. Sci. 47(4), 417–422 (2008). View at Publisher · View at Google Scholar · View at ScopusGoogle Scholar
  79. 79.
    Churchill, S.W.: A comprehensive correlating equation for laminar assisting forced and free convection. AIChE J. 23, 10–16 (1977)CrossRefGoogle Scholar
  80. 80.
    Shang, D.Y.: Theory of heat transfer with forced convection film flows. Springer, Berlin, Heidelberg (2011)CrossRefzbMATHGoogle Scholar
  81. 81.
    Shang, D.Y.: Free Convection Film Flows and Heat TransferModels of Laminar Free Convection with Phase Change for Heat and Mass Transfer Analysis. Springer, Berlin, Heidelberg (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.OttawaCanada
  2. 2.Department of Ferrous MetallurgyNortheastern UniversityShenyangChina

Personalised recommendations