Transient free convection flow past a vertical flat plate subject to a sudden change in surface temperature

Abstract

The transient free convection boundary-layer flow of a viscous and incompressible fluid adjacent to a semi-infinite vertical flat plate is investigated. It is assumed that for time τ < 0 a steady state boundary layer has been obtained in which there is a uniform temperature T∞ at large distances from the plate and the plate is at a temperature T 2. Then at τ = 0 the temperature of the plate is suddenly changed to T 2 and maintained at this value for τ > 0. The solution is dependent upon two parameters, namely the ratio of the final temperature above ambient to the initial temperature above ambient, R = ΔT 2/ ΔT 1 = ( T 2 - T ∞)/( T 1 - T ∞) and the Prandtl number Pr. An analytical solution is presented which is valid at small values of τ. 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 physically acceptable, to the finite-difference equations associated with the matching technique applied for times beyond that at which the step-by-step method breaks down. Results have been obtained for a range of values of the parameter R, when Pr = 1.