Abstract
This paper presents a result of numerical analysis for laminar natural convective heat transfer in a porous homogeneous medium inside a rectangular cavity with two uniformly heated hot walls vertically and two horizontal surfaces bounded as follows, 1) Model I: the open upper surface is permeable and cooled with constant heat transfer coefficient, while the closed bottom surface is non-permeable and insulated, 2) Model II: the closed upper surface is non-permeable and cooled with constant heat transfer coefficient, while the open bottom surface is permeable and insulated. A set of the partial differential equations (mass continuty equation, momentum equation of Darcy's flow, energy equation and fluid density equation) describing this cavity model in two dimensional laminar constant properties flow field is transformed into a set of non-dimensional equations using the appropriate parameters and then approximated into the two finite difference equations of non-dimensional temperature θ and stream function Ψ by the central finite-difference in the main. These F.D. equations of θ and Ψ are solved using the successive over-relaxation method at first θ and succeed to Ψ on the boundary conditions of the cavity Model I or II in the range of Rayleigh number Ra from 1.0 to 300 and aspect ratio A from 0.25 to 4, respectively. The caluculated results are presented in the terms non-dimensional stream function Ψ, temperature θ, velocity U, velocity V and the Nusselt number for Model I and Model II. Therefore, some characteristics of natural convective heat transfer and flow field inside the porous cavity are revealed and correlations of average heat transfer coefficient depended on Ra and aspect ratio A are obtained as follows, Model I for conductive region, Nu_m=0.415A^<-1.0>(1<Ra<20,0.25≦A≦4,H_L=1) for convective region, Nu_m=0.925×10^<-3>Ra^<1.7>A^<-1.0>(25<Ra<300,1≦A≦4,H_L=1) Model II for conductive region, Nu_m=0.415A^<-1.0>(1<Ra<20,0.25≦A≦4) These results of this study are available to understanding of the local and total heat transfer behavior and flow mechanism inside the porous cavity which is assumed as a heat storage tank for air conditioning use.
