Mixed-convection flow and heat transfer in a square enclosure around a rotating hot cylinder immersed in a Phan-Thien-Tanner viscoelastic fluid

This paper for the first time conducted numerical simulations for the mixed convective flow and heat transfer with a viscoelastic fluid within a square enclosure containing a rotating cylinder. The flow regime was considered laminar, two-dimensional, and transient, and the Phan-Thien-Tanner (PTT) model, recognized as one of the most accurate nonlinear models for viscoelastic fluids, was used to describe the viscoelastic fluid behavior, mathematically. Solving nonlinear fluid equations, predicting the complex properties of viscoelastic fluids using the constitutive equation of the PTT model, and considering viscous dissipation were the challenges of this research. Additionally, the paper addressed the numerical divergence at high Weissenberg numbers using a logconformation approach based on a logarithmic variable change in the polymer stress equation. The effects of the Richardson, Weissenberg, and Brinkman numbers and the ratio of polymeric viscosity to total viscosity on fluid flow and heat transfer were investigated by solving the nonlinear equations via the finite volume method. This was accomplished using the rheoHeatFoam solver within the OpenFOAM software. Local and average heat transfer characteristics around the rotating cylinder were fully studied. The results showed that elevating the Weissenberg number enhances the shear -thinning effect and diminishes the effective viscosity of the fluid by 63 %, resulting in a 54 % reduction in both the shear stress around the cylinder and the frictional torque applied to it, as well as a decrease in the viscous dissipation. Furthermore, increasing the Weissenberg number raised the Nusselt number from -1.33 to 3.32, signifying a complete reversal in the direction of heat transfer. However, the shear -thinning effect became negligible when the Weissenberg number exceeded 100. Moreover, the tangential normal stress significantly increased with an increase in the Weissenberg number up to one. However, as the Weissenberg number increased from 1 to 100, there was a significant decline in the tangential normal stress. Consequently, at very high Weissenberg numbers, the tangential normal stress approached zero, resembling a Newtonian fluid.