Effect of the temperature difference aspect ratio on natural convection in a square cavity for nonuniform thermal boundary conditions

The present numerical investigation deals with steady natural convection flow in a closed square cavity when the bottom wall is sinusoidal heated and vertical walls are linearly heated, whereas the top wall is well insulated. In the nonuniformly heated bottom wall maximum temperature T_H attains at the center of the bottom wall. The sidewalls are linearly heated, maintained at minimum temperature T_c at top edges of the sidewalls and at temperature T_h at the bottom edges of the sidewalls, i.e., T_c≤T_h≤T_H. Nonlinear coupled PDEs governing the flow have been solved by the penalty finite element method with biquadratic rectangular elements. Numerical results are obtained for various values of Prandtl number (Pr) (0.01≤Pr≤10) and temperature difference aspect ratio A =[(T_h-T_c)/ (T_H-T_c)] (0≤5A≤1) for higher Raleigh number Ra =10⁵. Results are presented in the form of streamlines, isotherm contours, local Nusselt number, and the average Nusselt number as a function of temperature difference aspect ratio A. The overall heat transfer process is shown to be tuned efficiently with suitable selection of A.