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Numerical solutions of, unsteady laminar free convection from an incompressible viscous fluid past a vertical cone with uniform surface heat flux is presented in this paper. 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 Prandtl number and semi vertical angle. 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.

Natural convection effects of the numerical solution for unsteady, laminar, free convection flow over an incompressible viscous fluid past a non-isothermal vertical cone with surface temperature T′w(x) = T′∞ + axn varying as power function of distance from the apex (x = 0) is presented here. 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 Prandtl number, semi vertical angle 0◦ < φ < 90◦ and n. 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.

An analysis is performed to study the effects of unsteady incompressible flow past a vertical cone with variable surface temperature T 0 w ðxÞ ¼ T 0 1 þ ax n varying as a power function of distance from the apex (x ¼ 0) and magnetic field applied normal to the surface. The dimensionless coupled partial differential boundary layer equations are solved numerically using an efficient and unconditionally stable finite-difference scheme of the Crank-Nicolson type. The velocity and temperature fields have been studied for various combinations of physical parameters (Prandtl number, Pr, exponent in power law variation in surface temperature, n, and magnetic field parameter, 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 the literature and are found to be in good agreement.