Group invariant solutions for nonlinear mathematical models of non-Newtonian fluids involving nano particles: A Lie symmetry approach

In this project, we aim to discuss the generalized Stokes model of a non-Newtonian fluid. We will consider the incompressible non-uniform flow of a non-Newtonian fluid over a moving porous boundary. The fluid flows into the porous region in the half space geometry. Our motive is to study the disturbance in the flow, which is induced due to impulsive motion of the porous boundary. Lie symmetry analysis will be carried out to calculate all possible Lie symmetry algebra associated with the modelled nonlinear partial differential equation describing the flow. We will utilize the Lie symmetry algebra to obtain the group invariant solutions of the governing model. We will provide the invariant solutions for the model in the form of closed-form exponential functions. Finally, we will observe the effects of the propitious flow parameters of the model through the graphical analysis of obtained results. Furthermore, we will study the time-dependent flow and heat transfer analysis of an incompressible, thermodynamically compatible non-Newtonian nano fluid model. Lie symmetry approach will be employed to the model equation to develop the group invariant solutions. The influence of the thermophysical parameters on the structure of velocity and temperature profiles will be studied in detail