On MHD 3D upper convected Maxwell fluid flow with thermophoretic effect using nonlinear radiative heat flux

In this study, three-dimensional upper-convected Maxwell fluid flow over a stretching surface in the presence of viscous dissipation and Joule heating is considered to examine the effects of thermophoresis and magnetohydrodynamics (MHD) on heat and mass transfer. Energy equation is formulated under the assumption of nonlinear radiative heat flux. Ordinary differential equations are deduced from the governing partial differential equations with the help of similarity transformation. These equations are then solved numerically using the shooting method, through the fourth-order Runge-Kutta integration procedure. To strengthen the reliability of our results, the MATLAB built-in function bvp4c is also used. Effects of some prominent physical parameters, such as Eckert number, Prandtl number, thermophoretic parameter, and magnetic parameter on the velocity, temperature, and concentration profiles are discussed graphically and numerically. It is found that concentration profile decreases for the higher values of thermophoretic parameter and Schmidt number. The heat flux rate is observed to enhance for increasing values of thermal radiation and Prandtl number.