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.