LIE GROUP ANALYSIS OF RADIATION NATURAL CONVECTION FLOW OVER AN INCLINED SURFACE IN A POROUS MEDIUM WITH INTERNAL HEAT GENERATION

Abstract

Lie group analysis is performed to study the heat transfer characteristics of the radiation natural convection flow of a heat generating fluid over a semi-infinite inclined surface embedded in a porous medium. The governing partial differential equations are transformed into a system of ordinary differential equations using scaling symmetries. The resulting system is solved numerically using a fourth-order Runge−Kutta method with the shooting technique. It is found that both the velocity and temperature increase significantly when the value of the heat generation parameter increases. The velocity increases and the temperature decreases with the increase in the porosity parameter. The thermal and momentum boundary layer thicknesses decrease when increasing the conduction−radiation parameter The local Nusselt number increases with the porosity and conduction−radiation parameter.