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

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.