On The solution of blasius problem by combined adomian decomposition method-integral transforms

Abstract

A boundary layer problem is a study of motion of fluid at a very thin layer. It is a single perturbation problem derived from the Navier-Stokes equations which are known as equations of motions for fluid in which the solution need to be solved. The Blasius equation is one of the basic equations in fluid dynamics that describes the steady flow of incompressible fluids over a semi-infinite flat plate. The aim of this study is to solve Blasius problem for two different boundary conditions. The first approach is to transform the Blasius boundary value problem into an initial value problem that introduces ??''(0) = ?? as a new initial condition. The method proposed to solve this problem for the two cases is by combining the Adomian Decomposition Method (ADM) with two integral transforms which are the Laplace and Elzaki transforms. Padè approximation is applied to determine the value of ??''(0) = ??. The values obtained are substituted into the respective Blasius series solutions and the behaviour of the solutions are studied. It is found that the Blasius solution of ??(??) and ??'(??) for both cases agree well with solutions from previous studies.