Skip to main content
SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
Heat Transfer of Laminar Mixed Convection of Liquid

Part of the book series: Heat and Mass Transfer ((HMT))

  • 823 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Gebhart, B., Jaluria, Y., Mahajan, R.L., Sammakia, B.: Buoyancy-induced Flows and Transport. Hemisphere, New York (1988)

    Google Scholar 

  2. Bejan, A.: Convective Heat Transfer. Wiley Inter Science, New York (1994)

    Google Scholar 

  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. 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. 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. Metais, B., Eckert, E.R.G.: Forced, mixed, and free convection regimes. J. Heat Transf. 86, 295–296 (1964)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  8. Acrivos, A.: Combined laminar free and forced convection heat transfer in external flows. AIChE J. 4, 285–289 (1958)

    Article  Google Scholar 

  9. Wilks, G.: Combined forced and free convection flow on vertical surfaces. Int. J. Heat Mass Transf. 16, 1958–1966 (1973)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Wilks, G.: Combined forced and free convection flow on vertical surfaces. Int. J. Heat Mass Transf. 16(10), 1958–1964 (1973)

    Article  MATH  Google Scholar 

  14. Mucoglu, A., Chen, T.S.: Mixed convection on inclined surface. J. Heat Transf. 101, 422–426 (1979)

    Article  Google Scholar 

  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)

    Article  ADS  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  18. Afzal, N., Hussain, T.: Mixed convection over a horizontal plate. J. Heat Transf. 106(1), 240–241 (1984)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  20. Yao, L.S.: Two-dimensional mixed convection along a flat plate. ASME J. Heat Transf. 109, 440–445 (1987)

    Article  Google Scholar 

  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)

    Article  ADS  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  27. Merkin, J.H., Pop, I.: Mixed convection along a vertical surface: similarity solutions for uniform flow. Fluid Dyn. Res. 30, 233–250 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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 Scholar

    Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. Hieber, C., Gebhart, B.: Mixed convection from a sphere at small Reynolds and Grashof numbers. J. Fluid Mech. 38(1), 137–159 (1969)

    Article  ADS  MATH  Google Scholar 

  35. Mucoglu, A., Chen, T.: Mixed convection about a sphere with uniform surface heat flux. J. Heat Transf. 100, 542–544 (1978)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  37. Tang, L., Johnson, A.T.: Flow visualization of mixed convection about a sphere. Int. Commun. Heat Mass Transf. 17(1), 67–77 (1990)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. 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. Bhattacharyya, S., Singh, A.: Mixed convection from an isolated spherical particle. Int. J. Heat Mass Transf. 51(5), 1034–1048 (2008)

    Article  MATH  Google Scholar 

  42. Gebhart, B., Pera, L.: Mixed convection from long horizontal cylinders. J. Fluid Mech. 45, 49–64 (1970)

    Article  ADS  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. Aydin, O., Kaya, A.: Mixed convection of a viscous dissipating fluid about a vertical flat plate. Appl. Math. Model. 31, 843–853 (2007)

    Article  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  55. Merkin, J.H., Mahmood, T.: Mixed convection boundary layer similarity solution: prescribed wall heat flux. ZAMP 40, 61–68 (1989)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  59. Yuge, T.: Experiments on heat transfer from spheres including combined natural and forced convection. J. Heat Transf. 82, 214–220 (1960)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. 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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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 Scopus

    Google Scholar 

  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 Scopus

    Google Scholar 

  79. Churchill, S.W.: A comprehensive correlating equation for laminar assisting forced and free convection. AIChE J. 23, 10–16 (1977)

    Article  Google Scholar 

  80. Shang, D.Y.: Theory of heat transfer with forced convection film flows. Springer, Berlin, Heidelberg (2011)

    Book  MATH  Google Scholar 

  81. Shang, D.Y.: Free Convection Film Flows and Heat Transfer—Models of Laminar Free Convection with Phase Change for Heat and Mass Transfer Analysis. Springer, Berlin, Heidelberg (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 136 Ingersoll Cres., Ottawa, ON, Canada

    De-Yi Shang

  2. Department of Ferrous Metallurgy, Northeastern University, Shenyang, China

    Liang-Cai Zhong

Authors
  1. De-Yi Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liang-Cai Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to De-Yi Shang .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Shang, DY., Zhong, LC. (2016). Introduction. In: Heat Transfer of Laminar Mixed Convection of Liquid . Heat and Mass Transfer. Springer, Cham. https://doi.org/10.1007/978-3-319-27959-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27959-6_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27958-9

  • Online ISBN: 978-3-319-27959-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation