A numerical study on three-dimensional conjugate heat transfer of natural convection and conduction in a differentially heated cubic enclosure with a heat-generating cubic conducting body

Abstract

A comprehensive numerical study has been conducted to investigate three-dimensional, steady, conjugate heat transfer of natural convection and conduction in a vertical cubic enclosure within which a centered, cubic, heat-conducting body generates heat. The physical model considered here assumes that a temperature difference exists across the enclosure (right cold wall and left hot wall) and the body generates a constant amount of heat. Under these conditions, the flow inside the enclosure is driven by two temperature differences: a temperature difference across the enclosure and a temperature difference caused by the heat source. A ratio of these two temperatures is a key parameter in this study. The steady, three-dimensional governing equations are written in a dimensionless form with dimensionless parameters that decide the heat transfer and flow characteristics in this system. The analysis is conducted by observing variations of the velocity vectors, pathlines, and isotherms for different Rayleigh numbers and temperature-difference ratios. The details of the three-dimensional flow and isotherms are described in order to investigate the effects of three-dimensionalities on the fluid flow and thermal characteristics in the enclosure. The variations of Nusselt numbers on the hot and cold walls are also presented to show the overall heat transfer characteristics inside the enclosure.