Instant nonsimilarity solutions of unsteady laminar boundary-layer heat transfer

An instant nonsimilarity method is proposed for the analysis of unsteady thermal boundary layers. The method is an improvement on the instant similarity method, which assumes that similarity solutions are obtained instantly by deleting time derivative terms that cause nonsimilarity in the boundary-layer energy equation. A basic feature of the nonsimilarity solution is that the nonsimilar terms in the conservation equations are retained without approximation, while those in derived auxiliary equations are selectively neglected. Therefore, more accurate results are obtained. The method is illustrated by analyzing the problems of unsteady laminar forced convection heat transfer from a rotating disk and at the two- and three-dimensional stagnation points due to a step change in surface temperature. The flow is steady and incompressible and has constant physical properties. Numerical results are compared with data from the literature. Excellent agreement is obtained at both short and long times.