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A Two-Equation Analysis of Convection Heat Transfer in Porous Media

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Abstract

This paper presents a two-equation analysis on the convection heat transfer in porous media based on the modeling developed by Carbonell and Whitaker (1984). The porous system under consideration is bounded by two parallel walls and heated uniformly from one side surface. The Darcy flow is imposed and the fully developed heat transfer is assumed. General solutions, which take into account the additional convective and conductive terms, are obtained for the temperature fields and the Nusselt number. The detailed studies are presented for the porous systems characterized by consolidated and unconsolidated circular unit cells. The results show that, for the consolidated unit cell case, a prediction without the additional convective term overestimates the heat transfer, while for the unconsolidated unit cell case, this effect is negligible. The additional conductive terms are also examined and found to act ‘conventionally’ as part of the conductive terms.

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References

  • Amiri, A. and Vafai, K.: 1994, Analysis of dispersion effects and non-thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media, Int. J. Heat Mass Transfer 37, 939-954.

    Google Scholar 

  • Amiri, A., Vafai, K. and Kuzay, T. M.: 1995, Effects of boundary conditions on non-Darcian heat transfer through porous media and experimental comparisons, Num. Heat Transfer A 27, 651-664.

    Google Scholar 

  • Amiri, A. and Vafai, K.: 1998, Transient analysis of incompressible flow through a packed bed, Int. J. Heat Mass Transfer 41, 4259-4279.

    Google Scholar 

  • Carbonell, R. G. and Whitaker, S.: 1984, Heat and mass transfer in porous media, In: Int. J. Bear and M.Y. Corapcioglu (eds), Fundamentals of Transport Phenomena in Porous Media, Martinus Nijhoff, Dordrecht, pp. 123-198.

    Google Scholar 

  • Chou, F. C., Su, J. H. and Lien, S. S.: 1992, A reevaluation of non-Darcian forced convection in cylindrical packed tubes, Fund. Heat Transfer Porous Media, ASMEHTD 193, 57-66.

    Google Scholar 

  • Hwang, G. J., Wu, C. C. and Chao, C. H.: 1995, Investigation of non-Darcian forced convection in an asymmetrically heated sintered porous channel, J. Heat Transfer 117, 725-732.

    Google Scholar 

  • Incropera, F. P. and Dewitt, D. P.: 1996, Fundamentals of Heat and Mass Transfer, 4th edn., Chap. 8, Wiley, NY.

    Google Scholar 

  • Kaviany, M.: 1995, Convective Heat Transfer in Porous Media, 2nd edn., Chap. 7, Springer-Verlag, NY.

    Google Scholar 

  • Lee, D. Y. and Vafai, K.: 1999, Analytical characterization and conceptual assessment of solid and fluid temperature differentials in porous media, Int. J. Heat Mass Transfer 42, 423-435.

    Google Scholar 

  • Levec, J. and Carbonell, R. G.: 1985, Longitudinal and lateral thermal dispersion in packed beds-Part I, AIChE J. 31, 581-590.

    Google Scholar 

  • Peterson, G. P. and Chang, C. S.: 1998, Two-phase heat dissipation utilizing porous-channels of high-conductivity material, J. Heat Transfer 120, 243-252.

    Google Scholar 

  • Quintard, M. and Whitaker, S.: 1993, One and two-equation models for transient diffusion processes in two-phase systems, in: Adv. Heat Transfer, Vol. 23, Academic Press, N.Y., pp. 369-465.

    Google Scholar 

  • Quintard, M. and Whitaker, S.: 1994a, Convection, dispersion, and interfacial transport of contaminants: homogenous porous media, Adv. Water Resour. 17, 221-239.

    Google Scholar 

  • Quintard, M. and Whitaker, S.: 1994b, Transport in ordered and disordered porous media II: generalized volume averaging, Transport in Porous Media 14, 179-206.

    Google Scholar 

  • Quintard M. and Whitaker, S.: 1995, Thermal equilibrium for transient heat conduction: theory and comparison with numerical experiments, Int. J. Heat Mass Transfer 38, 2779-2796.

    Google Scholar 

  • Quintard, M., Kaviany, M. and Whitaker, S.: 1997, Two-medium treatment of heat transfer in porous media: numerical results for effective properties, Adv. Water Resour. 20, 77-94.

    Google Scholar 

  • Vafai, K., Alkire R. L. and Tien, C. L.: 1985, An experimental investigation of heat transfer in variable porosity media, J. Heat Transfer 107, 642-647.

    Google Scholar 

  • Wakao, N. and Kaguei, S.: 1982, Heat and Mass Transfer in Packed Beds, Gordon and Breach Science Publishers, N.Y.

    Google Scholar 

  • Zanotti, F. and Carbonell, R. G.: 1984, Development of transport equations for multiphase systems-III. Application to heat transfer in packed beds, Chem. Engng Sci. 39, 299-311.

    Google Scholar 

  • Zhang, H. Y., Huang, X. Y. and Liu, C. Y.: 1999, Studies of convection heat transfer in porous media characterized by straight ducts, In: Proc. 5th ASME/JSME Thermal Engineering Joint Conference, San Diego.

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Authors and Affiliations

  1. School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore

    H. Y. Zhang & X. Y. Huang

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  1. H. Y. Zhang
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  2. X. Y. Huang
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Zhang, H.Y., Huang, X.Y. A Two-Equation Analysis of Convection Heat Transfer in Porous Media. Transport in Porous Media 44, 305–324 (2001). https://doi.org/10.1023/A:1010774630459

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