Lie-Group Analysis of Flow and Heat Transfer of a Dissipating Fluid Past Stretching/Shrinking Surfaces with Variable Viscosity and Non-Uniform Heat Flux

Abstract

The effects of surface mass flux (suction/injection) and variable viscosity on free-forced convection along a stretching or shrinking permeable plate embedded in a saturated porous medium are investigated through Lie-group analysis for steady two-dimensional flow in this paper. Assumptions are made that the fluid viscosity varies as a linear function of temperature and the heat flux through the plate wall varies with power law of the distance from the edge of the plate in a thermally radiating and incompressible fluid. The governing equations are tackled by means of Lie-group scaling transformation as to obtain a system of ordinary differential equations. Using Runge-Kutta-Gill scheme along with the shooting iteration technique, the resultant boundary-value problem is integrated numerically for different values of the physical fluid flow parameters. Comparisons between other previously published works with the present study were carried out for special cases and excellent agreements were demonstrated. The effect of moderate Prandtl number for a shrinking sheet is to reduce not only the velocity and temperature of the fluid but also the wall temperature gradient. Findings reveal that the wall friction parameter (skin-friction coefficient) and local heat transfer rate (Nusselt number or inverse wall temperature) increase with viscosity variation parameter aside the significant dependence on other emerging flow controlling parameters.