Mathematical Modelling of Variable Viscosity Hydromagnetic Boundary Layer Flow with Thermal Radiation and Newtonian Heating

Abstract

Magnetohydrodynamic (MHD) boundary layer flow for a variable viscosity fluid subject to thermal radiation and Newtonian heating has numerous applications in industry and engineering such as designing of cooling systems in electronic devices, cooling of nuclear reactors, solar energy harvesting, thermal insulation, heat exchangers and in geothermal reservoirs. Heat transfer by thermal radiation is of significance to engineering processes that occur at high temperature and plays a major role in designing of equipment used in Nuclear reactors, gas turbines and equipment for propelling air crafts, missiles, satellites, and rockets. In this study, we use the fourth-order Runge-Kutta method and the shooting technique to find the numerical solution to the equations of fluid flow governing the boundary layer flow of a varying viscosity electrically conducting fluid that is subjected to a constant magnetic field in the presence of thermal radiation and Newtonian heating. The graphical results depicting the effects of various thermophysical parameters on the velocity and temperature profiles of the fluid are presented and then discussed quantitatively. From the study, we note that the velocity of the fluid increases with the increase in the values of the magnetic parameter and variable viscosity parameter. Furthermore, the temperature of the fluid increases with an increase in the values of the magnetic field parameter, Brinkmann number and local Biot number and decreases with the increase in thermal radiation parameter and variable viscosity parameter.