Impact of nonlinear thermal radiation on nonlinear mixed convection flow near a vertical porous plate with convective boundary condition

Abstract

This study presents similarity solution for boundary layer flow near a vertical porous plate with combined effects of nonlinear density variation with temperature and nonlinear thermal radiation. To accurately predict the flow phenomenon near the porous plate, the convective boundary condition is considered at the plate surface. The two-dimensional partial differential equations are transformed to ordinary differential equations through the similarity transformation. The resulting ordinary differential equations are solved numerically in Maple software using the Runge–Kutta–Ferhlberg fourth-fifth order (RKF45) algorithm. The influence of the inherit parameters like the nonlinear thermal radiation parameter, suction/injection parameter, nonlinear Boussinesq approximation parameters, local convective heat transfer parameter, local Grashof number, and Prandtl number governing the fluid behaviour is discussed. We found that the rate of heat transfer improves with the injection and nonlinear thermal radiation parameter whereas decreases with suction, local convective heat transfer parameter and local Grashof number when air and mercury are used as the working fluids. Furthermore, with the growth in the values of local Grashof number, convective heat transfer parameter and nonlinear thermal radiation parameter and in the presence of suction/injection, the porous plate surface friction witnessed an observable growth. Suction growth plays a supportive role on the velocity curve near the porous plate but a contrary trend is seen in the free stream. The temperature distribution also decays with suction augment. Injection growth is inversely proportional to the velocity profile near the porous plate but we recorded the opposite phenomenon in the free stream.