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Lie group analysis of heat flux effect on MHD second slip flow for a slightly rarefied gas past a stretching sheet with heat generation

Megahed Ahmed M., Abdel-Rahman Reda G.

Technical Sciences / University of Warmia and Mazury in Olsztyn

2019

nr 22(1)

45--59

The present paper discusses steady MHD second order slip flow and heat transfer for a slightly rarefied gas due to an impermeable stretching sheet with heat flux and internal heat generation. By using the Lie group analysis, new similarity transformations are obtained. Employing these transformations, allows the partial differential equations governing the problem to transform into a system of ordinary differential equations which are later treated numerically using shooting method. Effects of the governing parameters on the dimensionless velocity and dimensionless temperature profiles are outlined graphically. Furthermore, results for the local skin-friction coefficient and the local Nusselt number are presented for some different values of the governing parameters in a tabular form. Also, results show that there is a strong dependency of the dimensionless temperature on the heat flux.

On the extension of Lie group analysis to functional differential equations

Oberlack M., Wacławczyk M.

Archives of Mechanics

2006

Vol. 58, nr 6

597-618

In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations. In order to perform the group analysis and deal with the functional derivatives, we extend the quantities such as infinitesimal transformations, prolongations and invariant solutions. For the sake of example, the procedure is applied to the functional formulation of the Burgers equation. The method can further lead to important applications in continuum mechanics.