Symmetry analysis on thermally magnetized fluid flow regime with heat source/sink

Abstract

In this article the Williamson fluid is equipped in a semi-infinite domain. The ongoing Williamson fluid is interacted with an externally applied magnetic field. The heat transfer individualities are taken into account in the presence of both the heat source and sink. The flow narrating differential system is obtained by coupling the most generally accepted differential equations namely, equation of momentum and equation of energy with constitutive relation of Williamson fluid model. For the better description of problem the Lie symmetry analysis is carried to obtain the scaling group of transformations for the Williamson fluid model rather than to go-on with so-called transformations available in literature. Such one parameter scaling group of transformations are utilized to drop the number of an independent variables. The reduced differential system is solved numerically by self-coded algorithm. The variations in primitive variables namely, the Williamson fluid velocity and Williamson fluid temperature are inspected and observations in this direction are provided by way of both graphical and tabular trends. The surface quantities namely, skin friction and Nusselt number are evaluated as well. It is observed that the Williamson fluid velocity is decreasing function of magnetic field parameter but Williamson fluid temperature shows an inciting values towards heat generation parameter. We believe that the symmetry treatment in this work will serve as a helping source for the unsolved complicated problems in field of fluid science.