Unified theory for the solutions of the unsteady thermal boundary-layer equation

Abstract

AbstractThe unsteady two-dimensional thermal boundary-layer equation linearized as by Lighthill is studied. Two different problems are considered mainly, one in Part I and the other in Part II. Part I deals with the solution when the temperature of the main stream is constant and that of the wall is unsteady and Part II when the temperature of the main stream is constant and the heat transfer from the wall is unsteady. Unified methods are developed from which the results for the stagnation flow and the flow along a flat plate, etc., can be derived as special cases. The results of the unsteady velocity boundary-layer equations analysed by Sarma are used and solutions are obtained in two cases, first, when the main stream is in steady motion and the wall is in an arbitrary motion and secondly when the main stream is in unsteady motion and the wall is at rest. The flat plate problem is considered in detail; the results agree with those given by Lighthill and Moore.