Effects of varying viscosity and thermal conductivity on steady MHD free convective flow and heat transfer along an isothermal plate with internal heat generation

Abstract

Purpose

Physical properties of a viscous fluid, e.g. viscosity and thermal conductivity change with temperature and in most of the studies concerned with natural convection, generally, the simultaneous effect of temperature dependent viscosity, thermal conductivity have been neglected. Hence, the purpose of this paper is to investigate the simultaneous effects of varying viscosity and thermal conductivity on free convection flow of a viscous incompressible electrically conducting fluid and heat transfer along an isothermal vertical non‐conducting plate in the presence of exponentially varying internal heat‐generation and uniform transverse magnetic field.

Design/methodology/approach

The governing equations of motion and energy are transformed into ordinary differential equations using similarity transformation. The resulting boundary valued, coupled and non‐linear differential equations are converted into system of linear differential equations and solved using Runge‐Kutta fourth order technique along with shooting method.

Findings

It was found that: fluid velocity decreases with the increase in magnetic parameter or Prandtl number; fluid temperature increases with the increase in magnetic parameter; velocity and temperature profiles increase due to increase in heat generation parameter; varying viscosity and thermal conductivity modifies the flow and heat transfer characteristic; and skin‐friction and heat transfer are affected by simultaneous change in viscosity and thermal conductivity in presence/absence of exponentially varying heat generation.

Research limitations/implications

The present study is applicable to an incompressible viscous fluid flow and heat transfer with linearly varying viscosity and thermal conductivity.

Originality/value

This paper provides useful information on the physical properties of a viscous fluid with regard to viscosity and thermal conductivity change with temperature.

Citation

Sharma, P.R. and Singh, G. (2009), "Effects of varying viscosity and thermal conductivity on steady MHD free convective flow and heat transfer along an isothermal plate with internal heat generation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 19 No. 1, pp. 78-92. https://doi.org/10.1108/09615530910922170