Technical Notes 3403 8. B. C. Sakiadis, Boundary layer behaviour on continuous solid surface : II. Boundary layer equations on continuous surface, A.1.Ch.E. Jl7,221-225 (1961). APPENDIX: INTEGRAL ANALYSIS An integral of momentum equation (12) between limits zero to co gives (Al) Introducing a function @such that 4(O) = 0, &co) = 1. The momentum integral (Al) yields AZ = 4’(O)/[B, -B,-@, -2B,)] (A3) where s 1. 3, = I-d,d[, B2 = 0 f 0m cb-Pdi. Using the above results it can be shown that f”(0) = (2E- l~[#‘(O)(~, -B,-E(B, -2&,))j”2 b = (2E- I)B,A. (‘44) lnl. J. Hair Moss Trunsjtr. Vol. 36, No. 13, pp, 3403-3406. 1993 Printed in Great Britain The relation (A4) shows that a solution does not exist for E > Em where s0 is given by Eg = l+(H-2)-l (A5) where H = PI/B2 is the shape factor (H > 2, Eg > 1). If one considers a trial velocity profile cb(i) = (31;-1?/2+ i $ 1; #4L’l = 1, i > 1 B, = 3j8, Bz = 39/280 then .Q = 2.46 and the solution is given by r(O) = (2s-- 1)(0,3536-0.1446~)“~ and for the trial profile (A61 9(1)=2i-21’+14. ict; $J(i)=1, c>r B, = 3/10, BZ = 37/315 c0 = 2.8 1 and the solution is given by f”(0) = (2~- 1)(0.365-0.130~)“~. (A7) The expression (A7) includes the two results (10) and (18) of ref. [2] as special cases. These solutions are good for E < 1 as for E = 1 the error is about 2% and F = 0 the error is about 5%. As E + - r*), the asymptotic behaviour of integral solution (A7) leads to f”(O) -+ -0.72(-E)“’ h-t -0.83(-&)“2. (A8f 0017-9310/9356.00+0.00 0 1993 Pergamon Press Ltd Three-dimensional natural convection in a vertical porous layer with hexagonal honeycomb core of negligible thickness YOSHIYUKI YAMAGUCHI, YUTAKA ASAKO and HIROSHI NAKAMURA Department of Mechanical Engineering, Tokyo Metropolitan University, Tokyo 192-03, Japan and MOHAMMAD FAGHRI Department of Mechanical Engineering, University of Rhode Island, Kingston, RI 02881, U.S.A. (Received 15 October 1991 and in~oi~orm 30 September 1992) INTRODUCTION HONEYCOMB structures are often used in thermal insulating walls. Inside such walls, the main mechanisms of heat trans- fer are by natural convection and radiation. A number of studies for natural convection heat transfer in such an air layer were investigated by Asako et al. [l-3]. If the air layer is filled with thermal insulations, such as glass wool, both convective and radiative heat transfer rates will decrease. A numerical analysis was reported by Asako et al. [4] to investigate heat transfer characteristics by natural con- vection in such a porous layer. The results were obtained for both conductive and adiabatic honeycomb core wall thermal boundary conditions. These condi~ons exist when the honey- comb core walls are good conductors and thick, and also when they are thermally insulated. For thermal insulating walls, it is required to reduce the heat loss through the honey- comb core walls. Then, the honeycomb core walls should be made as thin as possible to reduce the heat conduction through it. The motivation for the present study is to analyse the case where the honeycomb core walls are assumed to be poor conductors and thin, such that the thermal wall boundary conditions approach the so-called ‘no-thickness’ wall boundary condition dictated by Nakamura et al. [5]. These three boundary conditions, ‘conduction’, ‘adiabatic’, and ‘no-thickness’, can be considered as three idealized ther- mal boundary conditions. Therefore, the heat transfer rate in a practical porous layer will have a value that lies within these three conditions. The numerical methodolo~ used in this study utilizes an