Presents a finite‐difference solution to transient free convection flow past a semi‐infinite vertical plate in which the plate temperature T¢w(x) varies as the power of the axial co‐ordinate in the form T¢• + axn. Gives numerical results for fluids with Prandtl numbers Pr = 0.7 (air) and Pr = 7 (water) for three representative exponent values under non‐uniform surface heating conditions. Finds that the time to reach the steady‐state increases as the value of n or Pr increases. The steady‐state local skin‐friction falls by increasing the exponent n and Pr; however, the steady‐state local Nusselt number increases with n at a distance along the plate far away from the leading edge but decreases with increasing n near the leading edge of the plate. Also, the average Nusselt number increases and the average skin‐friction decreases as n increases because of enhanced heating of the plate.

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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.

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