Fully developed flow of a modified second grade fluid with temperature dependent viscosity

In this paper we will study the fully developed flow of a modified (and sometimes referred to as the generalized) second grade fluid down an inclined plane. The reasons for using such a model for the flow of non-Newtonian fluids are (i) the capability of predicting the normal stress differences and (ii) allowing for the possibility of shear dependent viscosity. The boundary value problem is solved numerically, and the special case of constant viscosity amends itself an exact solution (as previously reported in the literature) which serves as a test case to check the accuracy of our numerical scheme. The velocity and temperature profiles are obtained for various dimensionless numbers, for the case where the viscosity is also a function of temperature.