Transient free convection past a semi-infinite vertical plate with variable surface temperature

Presents a finite-difference solution transient free convection flow past a semiinfinite vertical plate in which the plate temperature T-w'(x) varies as the power of the axial co-ordinate in the form T-infinity' + ax(n). 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 it 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.