Unsteady Variable Thermal Conductivity Gravity Flow of a Power-Law Fluid with Viscous Dissipation through a Porous Medium

Abstract

In this work, the unsteady variable thermal conductivity gravity flow of a power-law fluid with viscous dissipation through a porous medium is examined. It is assumed that the fluid has variable temperature-dependent viscosity. The modified Darcy’s law is considered together with the equation of energy transfer in such media. The governing partial differential equations were transformed into ordinary differential equations in terms of a suitable similarity variable. Criteria for existence and uniqueness of solution are formulated. Central finite difference technique and Galerkin weighted residual method were employed to solve the resulting non-linear equations. The effects of variable viscosity parameter, Reynolds number, Brinkman number, Prandtl number, Peclet number, and those of viscous dissipation parameter on the flow system were reported graphically.

Keywords: Non-Newtonian fluid , Weighted residual method, Power-law fluid and Viscous dissipation.