Numerical study on transient heat transfer and fluid flow of natural convection in an enclosure with a heat-generating conducting body

A comprehensive numerical study has been conducted to investigate transient heat transfer and flow phenomena of natural convection of three different fluids of sodium, air, and water in a vertical square enclosure within which a centered squared, heat-conducting body generates heat. The physical model considered here is that a temperature difference exists across the enclosure (right cold wall and left hot wall) all the time and the body generates a constant amount of heat at an initial dimensionless time of tau less than or equal to 0. At time tau > 0 the amount of heat generated by the body is suddenly increased to 10 times as large as that at time tau less than or equal to 0. Under this situation, 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. We also consider the effects of Prandtl number and thermal conductivity ratio on the heat transfer and flow in the enclosure. The unsteady and hue-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 proceeds by observing variations of the streamlines and isotherms with respect to the dimensionless time for different Rayleigh numbers, temperature-difference ratios, Prandtl numbers, and thermal conductivity ratios. The variations of average Nusselt numbers on the hot and cold walls are also presented with respect to the dimensionless time, to show the transient behavior of overall heat transfer characteristics inside the enclosure.