Flow and heat transfer analysis of a special third grade fluid over a stretchable surface

Abstract

In this article, the flow and heat transfer of a special non-Newtonian third grade fluid over a stretching sheet with velocity $u_{w}(x) \approx x^{1/3}$ is investigated. The Lie group analysis has been carried out to find the relevant similarity variables that reduce the governing momentum and energy equations into a system of nonlinear ordinary differential equations (ODEs). The reduced boundary value problem is governed by the dimensionless stretching sheet parameter ($\lambda$), the non-Newtonian parameter (k), the Prandtl number (Pr) and the temperature power-law index (s). Previous numerical studies of the special third grade fluid have led to many hypotheses about the existence and behaviour of the solutions. The objective of this article is to verify these conjectures. The topological shooting argument has been used to prove the existence of the resulting momentum boundary layer equation. We proved that the governing equation has a unique and monotonic solution for any $k,\lambda >0$. Due to the absence of analytic solutions, the resulting equations are then solved numerically using the shooting technique. The rate of heat transfer increases as $\lambda ,~k,~Pr$, and s increase, but the opposite behaviour is found for the velocity profile.