Analysis of forced convection in pipes and channels with the simplified Phan-Thien–Tanner fluid

Analytical solutions are derived for the temperature distribution and heat transfer coefficient in forced convection of a viscoelastic fluid obeying the simplified Phan-Thien–Tanner constitutive equation in laminar pipe and plane channel flows. The results are valid for fully developed thermal and hydrodynamic flow conditions with a constant heat flux imposed at the wall and include the investigation of the effects of viscous dissipation. A nonvanishing value of the extensional parameter of the fluid model is shown to be essential for the solution to differ significantly from that for a Newtonian, or an elastic fluid without extensibility. Elasticity, only when combined with extensibility, is shown to increase the heat transfer and to reduce the range of temperatures present inside a duct. These beneficial effects of fluid elasticity are enhanced by viscous dissipation.