On Lie symmetry mechanics for Navier–Stokes equations unified with non-Newtonian fluid model: A classical directory

It is noticed that the most of the researchers having affiliation with the field of fluid science formulate the physical problems by coupling the constitutive relation of the fluid models with the Navier–Stokes equations. The ultimate system of partial differential equations in this direction becomes non-linear in nature due to which investigators always faced problem to narrate the flow field properties. Therefore, in this article we propose the symmetry toolkit to obtain the one parameter group of transformations for the flow controlling differential equations rather than to move-on with the so-called transformations available in literature. To propose idea we have considered the thermally magnetized Williamson fluid flow field along with heat source/sink and chemical reaction effects. The mathematical model is constructed by coupling the constitutive relation of Williamson fluid model with the Navier–Stokes equations in terms of partial differential equations. Such equations are reduced into system of ordinary differential equations by using self-constructed scaling group of transformations via symmetry analysis. The reduced system is solved by numerical algorithm. The key observations are added by means of graphs and tables. It is observed that both Weissenberg number and Hartmann number has same impact of Williamson fluid velocity. Further, Williamson fluid concentration reflects decline magnitude towards higher values of both Schmidt number and chemical reaction parameter. It is well trusted that the structuring of one parameter group of transformations for the particular flow problem will be helpful to report complete description as compared to utilizing the so-called transformations from an existing work.