Constant Wall Temperature Forced Convection in Pipes with the Simplified Phan-thien—tanner Fluid

The fully-developed thermal and hydrodynamic steady laminar pipe flow of the SPTT fluid is here investigated for the constant wall temperature boundary condition, assuming constant properties and negligible axial conduction. Two limiting conditions were identified: the solution pertaining to the equilibrium between axial convection and radial conduction of thermal energy, and the solution of the equilibrium of radial conduction of energy and energy production by viscous dissipation. Whereas for the first problem the solution was obtained by a successive approximation method, yielding results within 0.3% of the exact solution, for the second problem the final result is exact.