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

O. J. JAYEOLA, S. S. OKOYA

Abstract


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.

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