Homotopy Perturbation Method for Analyzing the Effect of Viscous Dissipation on Steady Natural Convection Couette Flow with Convective Boundary Conditions

This research article presents an analytical study of convective flow in a vertical channel with convective boundary conditions. Because of the nonlinear nature of the governing energy and momentum equations, the homotopy perturbation method was employed. The effects of various physical parameters on temperature and velocity profiles are illustrated in Figures 2 to 9, and a comparison table is provided to validate the results. Notably, both temperature and velocity distributions increased with higher viscous dissipation. Furthermore, the velocity profile decreased with an increase in the Biot number, while the temperature profile adjacent to the plate increased as the Biot number grew. Shear stress also exhibited an upward trend with rising viscous dissipation. Finally, an increase in the Grashof number and Biot number is found to elevate the skin friction on both plates. The mean temperature is higher when air is used as the working fluid compared to mercury. To validate this study, the temperature and velocity results were compared with previously published work, showing excellent agreement. This confirms the efficiency of the Homotopy Perturbation Method in solving coupled and nonlinear system of differential equations. Additionally, it was observed that both temperature and velocity increase with a rise in the Prandtl number, attributed to the dominance of momentum diffusivity over thermal diffusivity.