Numerical Solutions of Unsteady Laminar Free Convection from a Vertical Cone with Non-Uniform Surface Heat Flux

Numerical solutions of, unsteady laminar free convection from an incompressible viscous fluid past a vertical cone with non-uniform surface heat flux q_w(x)=ax^m varying as a power function of the distance from the apex of the cone ( x = 0 ) is presented. Here m is the exponent in power law variation of the surface heat flux. The dimensionless governing equations of the flow that are unsteady, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicolson type. The velocity and temperature fields have been studied for various parameters viz. Prandtl number Pr , semi vertical angle ϕ and the exponent m . The local as well as average skin-friction and Nusselt number are also presented and analyzed graphically. The present results are compared with available results in literature and are found to be in good agreement