Flow Past a Suddenly Cooled Vertical Plate

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Abstract
In this paper a solution of the unsteady free convection boundary layer equations is presented. It is assumed that for time t' < 0 that the steady state temperature and velocity have been obtained in the boundary layer on a semi-infinite vertical heated plate. At time t'= 0 the temperature of the plate is reduced to that of the surrounding fluid. Three distinct phases in the temporal development of the flow are considered. For t' ≪ 1 an analytical solution is obtained showing the initial decay of the boundary layer which is by means of diffusion outwards and convection from the plate. The boundary layer disappears as t' → ∞ and an analytical solution is obtained showing this approach. The matching of these two limiting analytical solutions has been obtained numerically by means of a step by step method. These results show good agreement with the analytical solutions which are valid at small and large times.

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