Natural Convection Coupled with Thermal Radiation in a Square Porous Cavity Having a Heated Plate Inside

Abstract

This study reports a numerical simulation of the natural convection combined with thermal radiation in a square porous cavity with a thin isothermally heated plate placed horizontally or vertically at its center. The vertical walls of the cavity are cooled while the horizontal ones are adiabatic. The governing equations were solved using a finite volume method on a uniformly staggered grid system. The computational results are presented in the form of isotherm and streamline plots and Nusselt numbers. The effects of the Darcy number ( \(10^{-5} \le \mathrm{Da} \le ~10^{-2})\) , plate length ( \(0.25\le D \le 0.75\) ) and the radiation parameter ( \(0 \le R_{d} \le 2\) ) are investigated for the Rayleigh number Ra =  \(10^{7}\) . It is found that the Darcy number, the plate length and the radiation parameter enhance the overall heat transfer rate across the cavity.

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