The Iterative Transformation Method for the Sakiadis Problem

TL;DR

This paper applies an iterative transformation method to solve the Sakiadis boundary layer problem, extending previous algorithms for the Blasius problem, and demonstrates its effectiveness through numerical results that align with existing literature.

Contribution

The paper extends the iterative transformation method to the Sakiadis problem, enabling solutions with homogeneous boundary conditions at infinity and coupling with Newton's method.

Findings

Numerical results agree with literature.

Method effectively handles boundary conditions at infinity.

Extension of the method to other boundary layer problems.

Abstract

In a transformation method the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. This paper is concerned with the application of the iterative transformation method to the Sakiadis problem. This method is an extension of the Toepfer's non-iterative algorithm developed as a simple way to solve the celebrated Blasius problem. As shown by this author [Appl. Anal., 66 (1997) pp. 89-100] the method provides a simple numerical test for the existence and uniqueness of solutions. Here we show how the method can be applied to problems with a homogeneous boundary conditions at infinity and in particular we solve the Sakiadis problem of boundary layer theory. Moreover, we show how to couple our method with Newton's root-finder. The obtained numerical results compare well with those available in literature. The main aim here is that any method developed for the Blasius, or the Sakiadis, problem might be extended to more challenging or interesting problems. In this context, the iterative transformation method has been recently applied to compute the normal and reverse flow solutions of Stewartson for the Falkner-Skan model [Comput. & Fluids, 73 (2013) pp. 202-209].