Numerical Investigation of Unsteady Mixed Convective Hydromagnetic Flow and Heat Transfer over a Vertical Stretching Surface with Variable Viscosity and Dissipation Effects

Résumé

An unsteady two-dimensional laminar mixed convection flow of an incompressible, viscous and electrically conducting fluid over a vertically stretching surface is numerically analyzed. The study accounts for the combined effects of temperature-dependent viscosity, viscous dissipation and Joule heating under the influence of an applied magnetic field. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations through appropriate similarity transformations. These equations are solved numerically using the Nachtsheim-Swigert shooting technique coupled with a fourth-order Runge-Kutta integration scheme to satisfy the asymptotic boundary conditions. Computations are performed for various values of the controlling physical parameters, and the influences of the variable viscosity parameter, unsteadiness parameter, Eckert number, Prandtl number, mixed convection parameter and Hartmann number on the velocity and temperature fields are illustrated graphically. In addition, numerical values of the skin-friction coefficient and Nusselt number are evaluated and presented in tabular form. Overall, the study demonstrates that the combined effects of variable viscosity, Joule heating, and viscous dissipation play a crucial role in controlling flow resistance and heat transfer characteristics over a vertical stretching surface. The findings provide useful physical insights and may serve as a reference for the design and optimization of MHD-based thermal systems encountered in industrial and engineering applications.