Lie group analysis of free convection flow over an inclined surface
Natural convection heat transfer past an inclined surface is investigated by Lie group analysis. Scaling symmetries are found and then the non-linear boundary layer equations with boundary conditions are transformed into a system of non-linear ordinary differential equations with appropriate boundary conditions. The resulting equations are solved numerically using the fourth-order Runge-Kutta scheme with Shooting method. Numerical results for the velocity and the temperature profiles are presented graphically for various values of parameters. It is observed that increasing Grashof number increases both the thermal and momentum boundary layer thicknesses and enhances the heat transfer rates. The velocity decreases with increase in the Prandtl number. Heat transfer rate decreases with Prandtl number.
Keywords: Lie groups, Natural convection, Inclined surface, Boundary layer.
