Finite Difference Simulation of Nonlinear Convection in Magnetohydrodynamic Flow in the Presence of Viscous and Joule Dissipation over an Oscillating Plate

Engineers and researchers are interested in the study of nonlinear convection, viscous dissipation, and Joule heating in various flow configurations due to their various applications in engineering processes. That is why the present study deals with the influence of nonlinear convection, viscous, and Joule dissipation of the temperature and velocity profile of incompressible fluid over a flat plate. In this study, the magnetic field acts perpendicular to the fluid flow and is supposed to be of uniform magnitude. Further, the Newtonian fluid, which is electrically conducting, passes over an infinite vertical flat plate under an oscillatory motion. The term representing the influence of the nonlinear convection phenomenon is integrated into the Navier-Stokes equation. The governing equations of the mentioned study were modeled in the form of non-linear PDEs and modified as non-dimensional equations via appropriate scaling analyses, which resulted in coupled and non-linear PDEs. For the numerical solution of the transformed non-linear PDEs, the finite difference method was applied. Finally, we present the effects of various flow parameters via graphical illustrations.

Automated summary

This study investigates the influence of nonlinear convection, viscous dissipation, and Joule heating on the temperature and velocity profiles of incompressible fluid over a flat plate. The governing equations are modeled as non-linear PDEs, which are solved numerically using the finite difference method.