Mixed Convection Heat Transfer of Air inside a Square Vented Cavity with a Heated Horizontal Square Cylinder

Abstract

The study of two-dimensional mixed convection from a heated square solid cylinder located at the center of a vented cavity filled with air (Pr = 0.71) is performed. The horizontal walls and the right vertical wall are kept adiabatic, while the left vertical wall is maintained at a constant temperature T _c . The flow is assumed to be laminar, steady and of constant physical properties except for the density in the buoyancy term, which follows the Boussinesq approximation. The developed mathematical model is governed by the coupled equations of continuity, momentum, and energy and is solved by the finite-difference method. This study investigates the effects of the outlet positions, Richardson numbers, Reynolds numbers, locations, and aspect ratios of inner square cylinder on the flow and the thermal fields. The parameters studied and their ranges are as follows: the Richardson number and Reynolds number are varied in the ranges from 0–10 and 50–200, respectively, location of the inner cylinder (0.25 ≤ L _X  ≤ 0.75, 0.5 ≤ L _Y  ≤ 0.75), and aspect ratios of 0.1, 0.2, 0.3, and 0.4. The present results show that the average Nusselt number along the heated surface of the inner square values increases with increasing values of the Reynolds and Richardson numbers. The effect of the locations of the inner square cylinder and aspect ratio is found to play a significant role in the streamline and isotherm patterns. An empirical correlation is developed by using the Nusselt number and the Reynolds and Richardson numbers. The results are compared and verified with previously published results, and good agreement is achieved.