hi. 1. .&a~ Mas.\ Trun&. Vol. 24, pp. 195-203 Pergamon Press Ltd. 1981. Printed in Greai Britain ~i7-93~0/81/020i~195 SOZ.W/O BOUNDARY AND INERTIA EFFECTS ON FLOW AND HEAT TRANSFER IN POROUS MEDIA K. VAFAI and C. L. TIEN Department of Mechanical Engineering, University of California, Berkeley, CA 94720, U.S.A. (Received 7 February 1980 and in revised form 11 June 1980) Abstract-The present work analyzes the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media. Specific attention is given to flow through a porous medium in the vicinity of an impermeable boundary. The local volume-averaging technique has been utilized to establish the governing equations, along with an indication of physical limitations and assumptions made in the course of this development. A numerical scheme for the governing equations has been developed to investigate the velocity and temperature fields inside a porous medium near an impermeable boundary, and a new concept of the momentum boundary layer central to the numerical routine is presented. The boundary and inertial effects are characterized in terms of three dimensionless groups, and these effects are shown to be more pronounced in highly permeable media, high Prandtl-num~r fluids, large pressure gradients, and in the region close to the leading edge of the flow boundary layer. NOMENCLATURE blowing coefficient, v,/uc; fluid’s heat capacity [Ws/kg K] ; Darcy number, K/L2 ; pore diameter [m] ; a function used in expressing inertia terms, defined in equation (1); a function used in expressing inertia terms, defined in equation (23); permeability of the porous structure [m2] ; horizontal extent of the external boundarv b-4; Nusselt number, defined in equation (30); pressure [N/m’] ; effective Prandtl number, vr/ae; Reynolds number, ucL/vf; Reynolds number based on permeability, uDJK1v.r ; temperature [K] ; free-stream temperature [K] ; external boundary temperature [K] ; x-component velocity [m/s] ; convective velocity, - (K/p)(dP/dx) [m/s] ; x-component of the Darcian velocity, [m/s] ; x-component of the pore velocity [m/s] ; velocity vector [m] ; Darcian velocity vector [m/s] ; pore velocity vector [m/s] ; y-component velocity [m/s] ; blowing velocity [m/s] ; spatial coordinate, horizontal [m] ; spatial coordinate, vertical [m]. Greek symbols effective thermal diffusivity, 3,,/p,c,6 [m’/s] ; porous media shape parameter, ,f6/K Cm-l]; porosity of the porous medium; dimensionless vertical length scale, Y~~x~Pr Reach) ; dimensionless temperature, (T- T,,J/ (r, - T,); effective thermal conductivity p/mK] ; fluid’s dynamic viscosity [kg/ms] ; fluid’s kinematic viscosity [m’/s] ; dimensionless horizontal length scale, x/L; fluid’s density [kg/m31 ; boundary parameter, (Pr/yL)* ; inertia parameter, GRe/y*L ; blowing parameter, BPr. denotes the ‘local volume average’ of a quantity. 1. INTRODUCTION SINCE the early work of Darcy in the nineteenth century, extensive investigations have been conducted on flow and heat transfer through porous media, covering a broad range of different fields and appli- cations such as ground-water hydrology, petroleum reservoir and geothermal operations, packed-bed chemical reactors, transpiration cooling, and building thermal insulation. Most analytical studies deal pri- marily with the mathemati~l formulation based on Darcy’s law, which neglects the effects of a solid boundary or the inertial forces on fluid flow and heat transfer through porous media [l-3]. These effects are expected to become more significant near the boun- dary and in high-porosity media, thus causing the appli~tion of Darcy’s law to be invalid [4-51. More- over, recent upsurge of utilizing high-porosity media in contemporary technology provides further impetus for a thorough understanding of the boundary and inertia effects. In spite of their common presence,