A Non-Iterative Transformation Method for Boundary-Layer with Power-Law Viscosity for Newtonian Fluids

TL;DR

This paper introduces a non-iterative transformation method for solving a boundary-layer problem with power-law viscosity in Newtonian fluids, extending the classical Blasius problem and providing a new computational approach.

Contribution

The paper develops a non-iterative transformation method applicable to boundary-layer equations with power-law viscosity, generalizing the T"opfer algorithm for the classical Blasius problem.

Findings

Successfully applied the method to the extended Blasius problem.

Obtained numerical results that compare favorably with existing literature.

Provided computed values of the missing initial condition across a range of parameters.

Abstract

In this paper, we have defined and applied a non-ITM to an extended Blasius problem describing a 2D laminar boundary-layer with power-law viscosity for Newtonian fluids. For a particular value of the parameter involved, this problem reduces to the celebrated Blasius problem and in this particular case, our method reduces to the T\"opfer non-iterative algorithm. In this case, we are able to compare favourably the obtained numerical result for the so-called missing initial condition with those available in the literature. Moreover, we have listed the computed values of the missing initial condition for a large range of the parameter involved, and for illustrative purposes, we have plotted, for two values of the related parameter, the numerical solution computed rescaling a reference solution.