Interaction of Surface Radiation with Conduction and Convection from a Vertical Channel with Multiple Discrete Heat Sources in the Left Wall

Abstract

This article reports the results of a numerical study of the problem of interaction of surface radiation with conduction and convection from a vertical channel equipped with three flush-mounted discrete heat sources in the left wall. The governing equations for temperature distribution along each of the two channel walls have been deduced based on appropriate energy balance between various energy interactions in which the channel is involved. Radiosity-irradiation formulation is employed to tackle radiation-related calculations, with the view factors involved therein obtained using Hottel's crossed-string method. The governing nonlinear partial differential equations are converted into algebraic form through a finite-volume-based finite-difference method, and are subsequently solved using Gauss-Seidel iterative technique. An optimum grid system, with 26 grids along each of the three discrete heat sources and 11 grids along each of the two non-heat source portions of the board, is used for discretization of the computational domain. The effects of various pertinent parameters, viz., aspect ratio, volumetric heat generation, thermal conductivity, surface emissivity, and convection heat transfer coefficient, on temperature distribution along the left board, maximum temperature in the channel, and relative contributions of convection and surface radiation to heat dissipation from the channel are probed.