Computational analysis of ohmic and viscous dissipation effects on MHD mixed convection flow in a vertical channel with linearly varying wall temperatures

Abstract

An analysis is carried out to investigate magnetohydrodynamic flow in a vertical channel formed by electrically conducting and non – conducting walls taking into account the effect of induced magnetic field. The phenomenon of heat transfer is also examined subject to the viscous and ohmic dissipations. The temperature of the channel wall increases or decreases linearly with x as [Formula: see text] in the direction of the fluid flow. The solutions are obtained analytically by perturbation method and numerically by finite element method. The solution is found to be dependent on the governing parameters which includes the Hartmann number, Rayleigh number, Brinkmann number, magnetic Prandtl number, and Reynolds number. The velocity, temperature, induced magnetic field, Nusselt number, and skin friction are evaluated for several set of values of these parameters. Increasing Brinkmann number augments both velocity and temperature profiles. Results reveal that the impact of Hartmann number and magnetic Prandtl number on the induced current density represents decreasing nature at the central region of the channel. The obtained velocity profile depicts inflection points for [Formula: see text] and the inflection points move towards the walls as the Rayleigh number enhances. Skin friction enhances with reference to Hartmann and magnetic Prandtl number at the wall [Formula: see text] while the reverse trend is observed at the wall [Formula: see text]. Effect of Rayleigh number and Brinkmann number on Nusselt number is also studied at the walls. This research combines computational fluid dynamic (CFD) simulations and artificial neural network (ANN) analysis. It is noted that the predicted data specified by the ANN model is in good agreement with the computed values of [Formula: see text] The average relative error in [Formula: see text] prediction is around [Formula: see text].