Heat transfer in a liquid film on an unsteady stretching surface

The momentum and heat transfer in a laminar liquid film on a horizontal str etching sheet is analysed. The governing time-dependent boundary layer equa tions are reduced to a set of ordinary differential equations by means of a n exact similarity transformation. The resulting two-parameter problem is s olved numerically for some representative values of the unsteadiness parame ter S for Prandtl numbers from 0.001 to 1000. The temperature is observed t o increase monotonically from the elastic sheet towards the free surface ex cept in the high diffusivity limit Pr --> 0 where the surface temperature a pproaches that of the sheet. A low stretching rate, i.e. high values of S, tends to reduce the surface temperature for all Prandtl numbers. The heat f lux from the liquid to the elastic sheet decreases with S for Pr less than or similar to 0.1 and increases with increased unsteadiness for Pr greater than or similar to 1. (C) 1999 Elsevier Science Ltd. All rights reserved.