Impact of temperature dependent heat source on MHD natural convection flow between two vertical plates filled with nanofluid with induced magnetic field effect

Abstract

This article presents a close form of solution to the magnetohydrodynamics free convection between two parallel vertical plates filled with nanoparticles with induced magnetic field effect. The surface of the channel is maintained at constant heat flux or constant temperature.The exact and the numerical solution is obtained through the method of undetermined coefficient and RKF45 in maple software respectively while the analytic solution is obtained through perturbation. The governing equations include the significant effects of the thermophoretic and Brownian motion parameters due to the presence of nanofluid. The role of the active parameters on the velocity, temperature, induced current density, concentration and induced magnetic field is illustrated using graphs. The results of the study showed that Brownian motion parameter Buoyancy ratio and the heat source parameter plays a supportive role on the velocity whereas other active parameters found to have decreasing effect on the velocity profile. Regarding the temperature distribution, the heat source parameter Brownian motion parameter and the thermophoretic parameter augment enhance the nanofluid temperature. The skin friction decreases with Hartmann number and magnetic Prandtl number augment but increases with Buoyancy ratio and heat source parameter