ORIGINAL SK Mahapatra Æ P Nanda Æ A Sarkar Analysis of coupled conduction and radiation heat transfer in presence of participating medium- using a hybrid method Received: 15 August 2003 / Published online: 8 June 2005 Ó Springer-Verlag 2005 Abstract The current study addresses the mathematical modeling aspects of coupled conductive and radiative heat transfer in presence of absorbing, emitting and isotropic scattering gray medium within two-dimensional square enclosure. The walls of the enclosure are consid- ered to be opaque, diffuse and gray. The enclosure comprised of isothermal vertical walls and insulated horizontal walls. A new hybrid method where the con- cepts of modified differential approximation employed by blending discrete ordinate method and spherical harmonics method, has been developed for modeling the radiative transport equation. The finite volume method has been adopted as the numerical technique. The effect of various influencing parameters i.e., radiation-con- duction parameter, surface emissivity, single scattering albedo and optical thickness has been illustrated. The compatibility of the method with regard to solving cou- pled conduction and radiation has also been addressed. List of symbols A W , A E , A S , A N Four face areas (West, East, South, North) I Radiation intensity (watt/m 2 ) I b Black body radiation intensity (=rT 4 /p) k Thermal conductivity (watt m 1 K 1 ) H Characteristic length (m) q R Radiation heat flux (watt/m 2 ) Q T Total heat flux q r Radiative heat flux q c Conductive heat flux RC Radiation-conduction parameter (=r T H 3 H/k) T Absolute temperature (K) T H, T_C Hot and cold wall temperatures X, Y Dimensionless co-ordinate. w i Quadrature weight associated with in any direction s i Greek Symbols a a Absorption coefficient (1/m) a s Scattering coefficient (1/m) b Extinction co-efficient (=a s +a a ) X Solid angle [sr] r Stefan Boltzman’s constant [5.67·10 8 watt m 2 K 4 ]  Wall emissivity n, g X and Y direction cosines x Single scattering albedo (a s/b ) q Reflectivity of the surface. s Total optical depth (=b H) h Dimensionless temperature (T/T H ) Subscripts: c - Conduction transfer R - Radiation transfer H, C, L - Hot wall, Cold wall, Bottom wall w, m - wall, medium 1 Introduction The transport of thermal radiation is an important mechanism of energy transport in numerous engineering S. Mahapatra Æ P. Nanda Mechanical Engg. Deptt., University College of Engineering, Burla, Orissa, India S. Mahapatra (&) Burla Engineering College Campus, Qrs No. 3R/32, Professor Colony, 768018, Orissa, India E-mail: swarupkumar_m@yahoo.com Fax: +91663-2430204 A. Sarkar Mechanical Engg. Deptt., Jadavpur University, Kolkata, India Heat Mass Transfer (2005) 41: 890–898 DOI 10.1007/s00231-004-0587-4