Heat transfer in a liquid film on an unsteady stretching surface

Abstract

The momentum and heat transfer in a laminar liquid film on a horizontal stretching sheet is analysed. The governing time-dependent boundary layer equations are reduced to a set of ordinary differential equations by means of an exact similarity transformation. The resulting two-parameter problem is solved numerically for some representative values of the unsteadiness parameter S for Prandtl numbers from 0.001 to 1000. The temperature is observed to increase monotonically from the elastic sheet towards the free surface except in the high diffusivity limit Pr→0 where the surface temperature approaches 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 flux from the liquid to the elastic sheet decreases with S for Pr≲0.1 and increases with increased unsteadiness for Pr≳1.