Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium

Hooman, Kamel and Merrikh, Ali A. (2006) Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium. Journal of Heat Transfer, 128 6: 596-600.


Author Hooman, Kamel
Merrikh, Ali A.
Title Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium
Journal name Journal of Heat Transfer   Check publisher's open access policy
ISSN 0022-1481
Publication date 2006-06
Sub-type Article (original research)
DOI 10.1115/1.2188510
Volume 128
Issue 6
Start page 596
End page 600
Total pages 5
Editor Y. Jaluria
Place of publication New York, N.Y., U.S.A.
Publisher A S M E International
Language eng
Subject C1
660401 Industry
0913 Mechanical Engineering
Abstract A theoretical analysis is presented to investigate fully developed (both thermally and hydrodynamically) forced convection in a duct of rectangular cross-section filled with a hyper-porous medium. The Darcy-Brinkman model for flow through porous media was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [1], is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.
Keyword Avionics
Aluminum foam
Cooling electronic equipment
forced convection
permeability
micro-porous
Thermodynamics
Engineering, Mechanical
Temperature-dependent Viscosity
Heat-transfer
Flow
References [1] Kays, W.M., and Crawford, M.E., 1993, Convective Heat and Mass Transfer, 3rd ed., McGraw-Hill, Inc. [2] Cheng, P., 1978, Heat Transfer in Geothermal Systems, Adv. Heat Transfer, 14, pp. 1-105. [3] Narasimhan A., and Lage, J.L., 2001 "Modified Hazen-Dupuit-Darcy Model for Forced Convection of a Fluid with Temperature-Dependent Viscosity," ASME J. Heat Transfer, 123, pp. 31-38. [4] Narasimhan, A., Lage, J.L., and Nield, D.A., 2001, "New theories for forced convection through porous media by fuids with temperature-dependent viscosity," ASME J. Heat Transfer, 123, pp. 1045-1051. [5] Brinkman, H.C., 1947, "A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles," App. Sci. Res., 1, pp. 27-34. [6] Nield, D.A., and Bejan, A., 1999, Convection in Porous Media, 2nd ed., Springer-Verlag, New York. [7] Lage, J.L., 1998, The Fundamental Theory of Flow through Permeable Media from Darcy to Turbulence, in Transport Phenomena in Porous Media (Eds. D.B. Ingham and I. Pop), Pergamon, Oxford, 1-30. [8] Vafai, K., and Tien, C.L., 1981, "Boundary and inertia effects on flow and heat transfer in porous media," Int. J. Heat Mass Transfer, 24, pp. 195-203. [9] Merrikh, A.A., and Mohamad, A.A., 2000, "Transient Natural Convection in a Porous Enclosure," J. Porous Media, 3, 2, pp. 165-178. [10] Haji-Sheikh, A., and Vafai, K., 2004, "Analysis of flow and heat transfer in porous media imbedded inside various-shaped ducts," Int. J. Heat Mass Transfer, 47, pp. 1889-1905. [11] Hooman, K., 2005, "Fully Developed Temperature Distribution in a Porous Saturated Duct of Elliptical Cross-Section, with Viscous Dissipation Effects and Entropy Generation Analysis," Heat Transfer Research, 36, pp. 237-245. [12] Holman, J.P., 2002, Heat Transfer, 9th Ed., McGraw-Hill, New York. [13] White, F.M., 1991, Viscous Fluid Flow, McGraw-Hill, Inc. [14] Kaviany, M., 1985, "Laminar flow through a porous channel bounded by isothermal parallel plates," Int. J. Heat Mass Transfer, 28, pp. 851-858. [15] Hooman, K., and Ranjbar-Kani, A.A., 2004, "A perturbation based analysis to investigate forced convection in a porous saturated tube," J. Comp. App. Math., 162, pp. 411-419.
Q-Index Code C1

 
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Created: Wed, 28 Mar 2007, 19:29:58 EST by Kamel Hooman on behalf of School of Engineering