The problem of heat transfer in the unsteady free convection flow over
a continuous moving vertical sheet in an ambient fluid has been inves
tigated. Both constant surface temperature and constant surface heat f
lux conditions have been considered. The nonlinear coupled partial dif
ferential equations governing the flow have been solved numerically us
ing the Keller box method and the Nakamura method which both give clos
ely similar solutions. The results indicate that the cooling rate of t
he sheet can be enhanced by increasing the buoancy parameter or the ve
locity of the sheet. It is found that a better cooling performance cou
ld be achieved by using a liquid as a cooling medium rather than a gas
. The overshoot in the velocity occurs near the surface when the buoya
ncy parameter exceeds a certain critical value.