ANALYTICAL SOLUTIONS FOR THE FLOW OF A REACTIVE THIRD-GRADE FLUID WITH TEMPERATURE DEPENDENT VISCOSITY MODELS IN A PIPE

This study focuses on the heat generation and various viscosity variational parameters of a third grade fluid flow in a circular pipe. The governing equations in cylindrical coordinates under quadratic heat generation is considered for three different viscosity models: constant viscosity, Reynold's and Vogel viscosity models. Perturbation technique is adopted and explicit, analytical expressions are derived for the dimensionless velocity and temperature of the fluid. These new analytical solutions are validated against the results obtained using numerical integration. Graphical results are presented and discussed quantitatively with respect to the competing effects of quadratic heat generation, viscous heating, pressure gradient and non-Newtonian material parameters. Thereafter, the analysis is focused on thermal criticality of physical parameters. The operating conditions of emerging parameters are discussed for the viscosity models.