Abstract
The effects of viscous dissipation on thermal entrance heat transfer in a parallel plate channel filled with a saturated popous medium, is investigated analytically on the basis of a Darcy model. The case of isothermal boundary is treated. The local and the bulk temperature distribution along with the Nusselt number in the thermal entrance region were found. The fully developed Nusselt number, independent of the Brinkman number, is found to be 6. It is observed that neglecting the effects of viscous dissipation would lead to the well-known case of internal flows, with Nusselt number equal to 4.93. A finite difference numerical solution is also utilized. It is seen that the results of these two methods, analytical and numerical, are in good agreement.
Similar content being viewed by others
References
Nield D A, Bejan A.Convection in Porous Media[M]. 2nd ed. Springer, New York, 1999.
Nield D A, Kuznetsov A V, Xiong M. Thermally developing forced convection in a porous medium: parallel plate channel or circular tube with walls at constant temperature[J].J Porous Media, 2004,7(1):19–27.
Nield D A, Kuznetsov, V V, Xiong M. The thermally developing forced convection in a porous medium: parallel plate channel or circular tube with walls at constant heat flux[J].J Porous Media, 2003,6(3):203–212.
Nield D A, Kuznetsov A V, Xiong M. Effect of local thermal non-equilibrium on thermally developing forced convection in a porous medium[J].Int J Heat Mass Transfer, 2002,45(25):4949–4955.
Lahjomri J, Oubarra A, Alemany A. Heat transfer by laminar Hartmann flow in thermal entrance region with with a step change in wall temperature: the Graetz problem extended[J].Int J Heat Mass Transfer, 2002,45(5):1127–1148.
Lahjomri J, Oubara A. Analytical solution of the Graetz problem with axial conduction[J].ASME J Heat Transfer, 1999,121(4):1078–1083.
Narasimhan A, Lage J L. Modified Hazen-Dupuit-Darcy model for forced convection of a fluid with temperature dependent viscosity[J].ASME J Heat Transfer, 2001,123(1):31–38.
Kreyszig E.Advanced Engineering Mathematics[M]. 4th ed. John Wiley & Sons, New York, 1979.
Shah R K, London A L.Laminar Flow Forced Convection in Ducts (Advances in Heat Transfer, Supplement 1)[M] Academic Press, New York, 1978.
Tannehill J C, Anderson D A, Pletcher R H.Computational Fluid Mechanics and Heat Transfer[M]. 2nd ed. Taylor & Francis, Inc. Bristol, 1997.
Nield D A, Kuznetsov A V. Effect of heterogeneity in forced convection in a porous medium: parallel plate channel or circular duct[J].Int J Heat Mass Transfer, 2000,43(22):4119–4134.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by ZHOU Zhe-wei
Rights and permissions
About this article
Cite this article
Hooman, K., Gorji-Bandpy, M. Laminar dissipative flow in a porous channel bounded by isothermal parallel plates. Appl Math Mech 26, 587–593 (2005). https://doi.org/10.1007/BF02466332
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02466332