hf. J. Heor Maw Tmsfw. Vol. 29, No. 3, pp. 403415, 1986 0017-9310/86$3.00+0.00 Printed in Great Britain 0 1986 Pcrgamon Prss Ltd. Mass and heat transfer by natural convection in a vertical slot filled with porous medium OSVAIR V. TREVISAN and ADRIAN BEJAN Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706, U.S.A. zyxwvutsrqpon (Received 25 February 1985 and injnalform 16 September 1985) Abstract-This paper reports an analytical and numerical study of natural convection heat and mass transfer through averticalporouslayer subjectedto uniformfluxesofheat andmassfrom theside.Theflowisdrivenby the combined buoyancy effect due to temperature and concentration variations through the porous medium. The first part of the study contains an analytical Oseen-linearized solution for the boundary-layer regime and I_.e = l,andasimilaritysolutionforheat-transfer-drivenflows(n = 0)andLe > l.Thesecondpart ofthestudy contains an extensive series of numerical experiments that validate the analytical results and provide heat and mass transfer data in the domain not covered by analysis. The numerical results cover the Rayleigh number range 20 < Ra < lo’, the buoyancy ratio range - 11 < n < 9, the geometric aspect ratio range 1 < H/L < 4 and the Lewis number range 0.03 < Le < 40. zyxwvutsrqponmlkjihgfedcbaZYXWV INTRODUCTION THE PURPOSE of this report is to summarize a fundamental analytical and numerical study of heat and mass transfer by natural convection in a porous medium saturated with fluid. The special feature of this study is the focus on flows driven by conditions of uniform heat and mass flux imposed along the two vertical side walls of the porous layer. This set of conditions comes closest to simulating the boundary conditions for heat and mass transfer in insulation systems exposed to thermal radiation heating (e.g. the migration of moisture through double walls filled with fibrous or granular insulation). Although as demonstrated by a number of recent monographs [l-3] the phenomenon of natural convection through porous media has received considerable attention, the bulk of the existing work has been devoted to pure natural convection heat transfer, not to phenomena driven by the combined buoyancy effect due to temperature and concentration variations through the porous medium. The necessary first step in elucidating the main features of the combined heat and mass transfer phenomenon addressed in this paper has just been reported in ref. [4], in which pure scaling arguments were used to identify and sort out the most basic scales that characterize the flow, temperature and concentration fields in the immediate vicinity of a single vertical surface imbedded in a porous medium of different temperature and concentration. In connection with the combined heat and mass transfer natural convection phenomenon of ref. [4], considerably more important from a practical standpoint is the configuration sketched in Fig. 1, namely, the vertical porous layer of finite thickness L and finite height zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA H. In the first phase of our work on this configuration [S], we modeled the two vertical side walls as impermeable surfaces with imposed constant temperature and concentration. We were able to show that numerical simulations of the phenomenon are in agreement with the results of the scale analysis conducted along the lines of ref. [4] for the single- surface configuration. However, due to the constant temperature and concentration imposed along the vertical boundaries, we were unable to develop closed- form analytical solutions for engineering heat and mass transfer calculations, to improve on the order-of- magnitude estimates produced by scale analysis. zyxwvutsrqponm insulated and impermeable 9” Y zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP ‘L 01 U 0 (^y=1/2 ) _ x 2.0) ^x= L/H) porous I I, J medium ? 1 H/2 ($=I insulated and lmpcrmrable FIG. 1.Schematic of a twodimensional porous layer subjected to uniform heat and mass fluxes in the horizontal direction. 403