Forced convection cooling enhancement by use of porous materials Y. Ould-Amer a , S. Chikh a , K. Bouhadef a , G. Lauriat b, * a Institut de G enie M ecanique, USTHB, B.P. 32, El Alia, Bab Ezzouar 16111, Algeria b Universit e de Marne-la-Vall ee, Cit e Descartes, Champs-sur-Marne, 77454 Marne-la-Vall ee Cedex, France Received 25 August 1996; accepted 6 December 1997 Abstract Results are presented for laminar forced convection cooling of heat generating blocks mounted on a wall in a parallel plate chan- nel. The eect on heat transfer of insertion of a porous matrix between the blocks is considered. The ¯ow in the porous medium is modeled using the Brinkman±Forchheimer extended Darcy model. The mass, momentum and energy equations are solved numer- ically by a control-volume-based procedure. The local Nusselt number at the walls of the blocks, the mean Nusselt numbers and the maximum temperature in the blocks are examined for a wide range of Darcy number and thermal conductivity ratio. The compu- tations are ®rst conducted for a single block, then for evenly mounted blocks. The results show that the insertion of a porous ma- terial between the blocks may enhance the heat transfer rate on the vertical sides of the blocks. Although the porous matrix reduces the heat transfer coecient on the horizontal face, signi®cant increases in the mean Nusselt number (up to 50%) are predicted and the maximum temperatures within the heated blocks are reduced in comparison with the pure ¯uid case. Ó 1998 Elsevier Science Inc. All rights reserved. Keywords: Forced convection cooling; Channel ¯ow; Porous medium; Electronic cooling International Journal of Heat and Fluid Flow 19 (1998) 251±258 Notation c height of the blocks C dimensionless height of the blocks C  c=H  c f ¯uid speci®c heat Da Darcy number Da  K=H 2  e thickness of the porous matrix E dimensionless thickness of the porous matrix E  e=H  F Forchheimer coecient in Eq. (3) f(d) function used in the energy equation h heat transfer coecient H channel height k e eective thermal conductivity k f thermal conductivity of the ¯uid k s thermal conductivity of the solid K permeability of the porous material l channel length L dimensionless channel length L  l=H  l 1 entrance length L 1 dimensionless entrance length L 1  l 1 ==H  l 2 length after last block L 2 dimensionless length after last block L 2  l 2 =H  Nu local Nusselt number Nu b mean Nusselt number for a block p pressure P dimensionless pressure P  p=q f U 2 0  Pr ¯uid Prandtl number Pr  m f =a f  q heat dissipation per cubic meter q  Q=cw Q heat dissipation per unit length in each block Re Reynolds number Re  q f U 0 H =l f  R k thermal conductivity ratio k s =k f or k e =k f  s spacing between the blocks S dimensionless spacing between the blocks S  s=H  T 0 temperature T dimensionless temperature T T 0  T 0 =Q=k f  T 0 inlet temperature u axial velocity U dimensionless axial velocity U  u=U 0  U 0 uniform inlet velocity v transverse velocity V dimensionless transverse velocity V  v=U 0  w block width W dimensionless block width W  w=H  x axial coordinate X dimensionless axial coordinate X  x=H  y transverse coordinate Y dimensionless transverse coordinate Y  y =H  Greek a thermal diusivity a  k=q f c f  e porosity U general dependant variable k inertial coecient k  F e=Da 1=2  * Corresponding author. 0142-727X/98/$19.00 Ó 1998 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 2 - 7 2 7 X ( 9 8 ) 0 0 0 0 4 - 6