Flow and heat transfer in Phan-Thien–Tanner viscoelastic fluid around a rotating hot cylinder in a square enclosure

Abstract

Flow and heat transfer problems in non-Newtonian fluids are considerably more complicated compared to Newtonian fluids due to their non-linear behavior and complex properties. This paper numerically studied the flow and heat transfer of a viscoelastic fluid around a hot rotating cylinder in a square enclosure. The Phan-Thien–Tanner (PTT) model, one of the most accurate models available to describe the behavior of viscoelastic fluids, was used to obtain the constitutive equations of the viscoelastic fluid, which were then solved by using the finite-volume method with the Rheoheatfoam solver of the OpenFOAM software. The log-conformation approach was employed to avoid the divergence problem at high Weissenberg numbers. Simulations were conducted to investigate the effects of the Weissenberg number, Brinkman number, Reynolds number, and the ratio of the polymeric viscosity to total viscosity on the behavior of fluid flow and heat transfer. The results showed that increasing the Weissenberg number led to a higher shear thinning effect, which decreased the fluid's effective viscosity and viscous dissipation near the cylinder. As a result, heat transfer from the cylinder increased, and the frictional torque applied to the cylinder decreased. However, the shear thinning effect was negligible when the Weissenberg number exceeded 100. Furthermore, the tangential normal stress significantly increased as the Weissenberg number increased up to one. However, with further increases in the Weissenberg number, the tangential normal stress reduced, eventually reaching close to zero at high Weissenberg numbers.