Pergamon ant. Comm. Heat Mass Tramfes Vol. 28, No. 1, pp. 77-86, 2001 Copyright 8 2001 Elsevier Science Ltd Printed in the USA. All tights reserved 07351933/01/!§-see front matter PII: SO7351933(01)00215-9 COMBINED CONDUCTION AND RADIATION HEAT TRANSFER IN A GRAY ANISOTROPICALLY SCATTERING PLANAR MEDIUM WITH DIFFUSE-SPECULAR BOUNDARIES C. K. Krishnaprakas and K Badari Narayana Thermal Systems Group ISRO Satellite Centre Bangalore 560 017, India Pradip Dutta Department of Mechanical Engineering Indian Institute of Science Bangalore 560 012, India (Communicated by A.R. Balakrishnan) ABSTRACT Coupled conduction and radiation heat transfer in a gray planar nonlinearly anisotropic scattering medium bounded between two plane parallel surfaces reflecting both diffusely and specularly is analyzed. The governing integrodifferential equations are solved by a numerical iterative method consisting of Numerov’s method to solve the energy equation and Chandarsekhar’s discrete ordinates method in conjunction with the Crank-Nicolson method to solve the radiative transfer equation. Convergence of the solution is enhanced by Ng-acceleration. The numerical algorithm described is found to be fast and reliable. Numerical results based on Sj2 method indicate that anisotropy plays an important role, and difference between the diffuse and specular reflections is found to be insignificant. Q 2001 Elsevier Science Ltd Introduction Heat transfer by coupled conduction and radiation in an absorbing, emitting and scattering planar medium is important in many areas such as in insulation practice employing evacuated multi-layer insulation packed with fillers (e.g. foams, fibers or powders). These insulations can be used in cryogenic and space applications, fluidized beds, optical engineering, solar engineering, nuclear engineering, and so on. Mathematical formulation of the problem leads to a nonlinear integrodifferential equation that presents difficulties in solution. Many investigators have proposed approximate solution methods in the past for various limiting cases such as optically thin, optically thick, conduction dominant, and radiation 77