Second grade Casson fluid flow with variable viscosity and thermal conductivity through a porous medium

Abstract

This work investigated the convective flow of a second grade Casson fluid through a non-Darcy porous medium under the influence of thermophoresis, Dufour and Soret effects. It is assumed that the viscosity and thermal conductivity are linearly functions of temperature. Similarity transformations were used to reduce the governing partial differential equations (PDE) to a system of nonlinear coupled ordinary differential equations (ODE). Runge Kutta of order four with shooting method was used to obtain the numerical solutions for the velocity, temperature and concentration profiles. The behaviour of the velocity, temperature and concentration distributions was examined using various values of dimensionless numbers like the thermophoresis parameter, τ, at different temperature conditions, porosity parameter Pp, viscoelastic parameter K2 and Prandtl number Pr. τ has no significant effect on velocity and temperature distributions when the heat induced into the system is negligible. Increase in Pp increased the Lorentz force and therefore decreased the velocity but increased the temperature and concentration distributions. Temperature increased with increase in k2 throughout the boundary layer.