Modeling the hydromagnetic transient three-dimensional stagnation point flow of a couple stress Casson fluid over a bi-directional stretching sheet

Abstract

A numerical study is performed to examine the magnetohydrodynamic effects on the transient three-dimensional stagnation point flow of a Casson fluid along a bi-directional stretching sheet. The physical model of the flow includes a sheet which is stretched in both the tangential directions and is thus called “bi-directional stretching”. The heat transfer mechanism includes the influences of space- and time-dependent non-uniform heat generation/absorption, as well as dissipation due to viscosity. The mathematical modeling of the problem involves the constitution of a set of coupled nonlinear boundary layer equations, together with suitable boundary conditions. The mathematical model thus developed is then subjected to suitable similarity transformations to arrive at a set of ordinary differential equations, which were then treated with the successive linearization method (SLM) to obtain approximate solutions for the velocity and temperature fields. A parametric study is carried out, and the results are discussed and presented graphically to analyze the behavior of the primary and secondary velocity distributions, as well as fluid temperature, along with significant physical quantities such as skin friction and Nusselt number for various values of the nondimensional parameters. Multiple quadratic regression analysis is also carried out to investigate the significance of parameters and to estimate the skin-friction and heat transfer coefficients.