Exponential Class of Similarity Solutions for the Hydromagnetic Falkner-Skan Equations

TL;DR

This paper derives a new class of similarity solutions for hydromagnetic Falkner-Skan equations with exponential external fields, using Lie symmetries, and explores their numerical and series solutions for various flow conditions.

Contribution

It introduces a novel exponential class of similarity solutions for hydromagnetic boundary layer equations without assuming external fields beforehand.

Findings

Derived new similarity reductions for exponential magnetic fields.

Numerically solved the resulting equations for different wall velocity profiles.

Obtained series solutions to analyze skin friction behavior under strong magnetic fields.

Abstract

A systematic search for the Lie point symmetries admitted by the steady hydromagnetic two-dimensional incompressible viscous flow boundary layer equation and associated boundary conditions is performed. Unlike previous works, the specific forms of the external velocity and transverse magnetic fields are not postulated from the very beginning. In this way a whole new class of similarity reductions for the problem is derived, for applied fields having an exponential nature. The corresponding hydromagnetic Falkner-Skan equation is numerically solved for different velocity profiles at the wall, considering stretching, expansion, injection or suction. For intense magnetic fields a series solution is derived and used to investigate the behaviour of the skin friction with respect to the initial conditions for both expanding and converging flows.