Effects of temperature-dependent viscosity and thermal conductivity on mixed convection flow along a magnetized vertical surface

Abstract

Purpose

The purpose of this paper is to report a numerical solution for the problem of steady, two dimensional boundary layer buoyant flow on a vertical magnetized surface, when both the viscosity and thermal conductivity are assumed to be temperature-dependent. In this case, the motion is governed by a coupled set of three nonlinear partial differential equations, which are solved numerically by using the finite difference method (FDM) by introducing the primitive variable formulation. Calculations of the coupled equations are performed to investigate the effects of the different governing parameters on the profiles of velocity, temperature and the transverse component of magnetic field. The effects of the thermal conductivity variation parameter, viscosity variation parameter, magnetic Prandtl number Pm_r, magnetic force parameter S, mixed convection parameter Ri and the Prandtl number Pr on the flow structure and heat transfer characteristics are also examined.

Design/methodology/approach

FDM.

Findings

It is noted that when the Prandtl number Pr is sufficiently large, i.e. Pr=100, the buoyancy force that driven the fluid motion is decreased that decrease the momentum boundary layer and there is no change in thermal boundary layer is noticed. It is also noted that due to slow motion of the fluid the magnetic current generates which increase the magnetic boundary layer thickness at the surface. It is observed that the momentum boundary layer thickness is increased, thermal and magnetic field boundary layers are decreased with the increase of thermal conductivity variation parameter =100. The maximum boundary layer thickness is increased for =100 and there is no change seen in the case of thermal boundary layer thickness but magnetic field boundary layer is deceased. The momentum boundary layer thickness shoot quickly for =40 but is very smooth for =50.There is no change is seen for the case of thermal boundary layer and very clear decay for =40 is noted.

Originality/value

This work is original research work.

Citation

Muhammad, A., Chamkha, A.J., Iqbal, S. and Ahmad, M. (2016), "Effects of temperature-dependent viscosity and thermal conductivity on mixed convection flow along a magnetized vertical surface", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 5, pp. 1580-1592. https://doi.org/10.1108/HFF-08-2014-0265