FEM-based numerical solutions for mixed convection MHD flow of fluid inside the square cavity having sinusoidal walls

This analysis deals with the steady and incompressible magnetohydrodynamics fluid flow by sinusoidal walls of a square cavity. Sinusoidal velocity and sinusoidal temperature at walls of the cavity are of great importance in engineering including solar collectors, air conditioners, and thermal effects in the buildings. Mixed convection is focused exhaustively as it is important in most engineering and geophysical phenomena. A numerical modeling method, finite element method (FEM) is operated to study the flow and heat transfer governed by continuity equations, Navier-Stokes equations, and temperature equations. These equations are converted to dimensionless form through suitable parameterization, which is tackled by FEM. The temperature and velocity profiles are displayed for a variety of parameters. This graphical study shows good convergent results of temperature and velocity for variation of involved parameters. In the end, the significant effects of the heat transfer rate are analyzed and discussed in terms of the average Nusselt number.