Disappearance of criticality for reactive third-grade fluid with Reynold's model viscosity in a flat channel

In this paper, we consider how a model for the motion with exponential viscosity of a third-grade fluid flowing between parallel plates, under the action of externally imposed pressure gradient, affects the fully developed and laminar reactive flow. The non-dimensional form of the coupled equations are solved numerically. The temperature distribution is presented for various viscosity variational parameters and the number is related to the Frank-Kamenetskii parameter. The criticality and disappearance of criticality (transition) of physical parameters and the competing effects of viscous dissipation, viscosity variational number, heat generation and non-Newtonian are discussed.