TRANSIENT FREE-CONVECTION FLOW PAST A VERTICAL FLAT-PLATE SUBJECT TO A SUDDEN CHANGE IN SURFACE-TEMPERATURE

The transient free convection boundary-layer how of a viscous and inco mpressible fluid adjacent to a semi-infinite vertical hat plate is inv estigated. It is assumed that for lime <(tau)over bar> < 0 a steady st ate boundary-layer has been obtained in which there is a uniform tempe rature T-infinity at large distances from the plate and the plate is a t a temperature T-1. Then at <(tau)over bar> = 0 the temperature of th e plate is suddenly changed to T,and maintained at this value for <(ta u)over bar> > 0 The solution is dependent upon two parameters, namely the ratio of the final temperature above ambient to the initial temper ature above ambient, R=Delta T-2/Delta T-1 = (T-2-T-infinity)/(T-1-T-i nfinity), and the Prandtl number Pr. An analytical solution is present ed which is valid at small values of <(tau)over bar>. A new phenomena in this class of problems that is obtained from the detailed numerical scheme is the existence of two solutions, only one of which is physic ally acceptable, to the finite-difference equations associated with th e matching technique applied for times beyond that al which the step-b y-step method breaks down. Results have been obtained for a range of v alues of the parameter R, when Pr = 1. (C) 1997 Elsevier Science Ltd.