Convective Heat Transfer in a Square Cavity with a Heat-Generating Body of Different Aspect Ratios

Abstract

The problem of flow and heat transfer in a square cavity with a heat source at the center has been numerically studied. For the cavity considered, the horizontal walls are insulated while the vertical walls are maintained at constant cold temperature and the heat source at the center is kept at a constant hot temperature. The principal partial differential equations of mass, momentum, and energy are solved by applying Finite Element Method to perform a parametric study. Numerical experiments was conducted for Rayleigh numbers (Ra) in the range; 10 2 to 10 7 for a heat generating (source) body of aspect ratios (AR) = 0.1-0.6 with steps of 0.1. Streamlines and Isotherm contours of the ensuing temperature and flow fields are presented together with the estimated Nusselt numbers (Nu) for a fluid (air at room temperature) with Prandtl number of 0.71. The results of the numerical experiment indicate that for a fixed AR, with increasing Ra, the heated fluid is transported to the top-half of the cavity; a region characterized by increased fluid motion due to convection of the less dense heated fluid. From the estimated Nu along the boundary of the heat source in this top-half region, heat transfer by convection is a generally dominant heat transfer mechanism, however, with increasing AR and due to decreasing mid-cavity temperature gradients, contributions of heat conduction to the fluid is steadily noticeable as a wide section of the obstacle is in contact with the fluid.