Forced convective heat transfer of nonlinear viscoelastic flows over a circular cylinder at low Reynolds inertia regime

摘要

In this paper, the forced convective heat transfer of viscoelastic fluid flow around a circular cylinder at a low Reynolds number is studied numerically. The effect of viscous dissipation on the problem is modeld which is the main innovative aspect of present study. The Phan-Thien-Tanner (PTT) model is used as the nonlinear constitutive equation. To avoid divergence and stabilize the numerical process in high elastic cases, the log-conformation approach is used. The results indicated that the Nusselt number (Nu) monotonically increases with increasing elasticity number (El), retardation ratio (beta), Prandtl number (Pr), and Brinkman number (Br) in a wide range. Both drag reduction (for El < 0.025) and drag enhancement (for El > 0.025) were seen in the numerical results. In high elastic flow regime (El > 10), due to the increased storing nature of viscoelastic fluid compared to the dissipative nature, drag coefficient (C-D) and Nu become constant, which causes the fluid to behave like a Newtonian fluid. The temperature-dependent properties were also investigated for all of fluid property, and the large effects of viscosity, and relaxation time were seen in hydrodynamic and thermal parameters. The contribution of normal stresses in viscous dissipation (VD) is much lower than shear stress, due to the lower values of corresponding components in deformation tensor. The elasticity influences the heat transfer by two mchanisms of convection empowering as an indirect way and viscous dissipation as a direct way. Increasing El, beta, and xi increases Nu via the convection mechanism (even at Br = 0), while Nu is decreased with epsilon. However, Nu increases with the variations of all the parameters, in presence of viscous dissipation. It was also seen that the heat transfer direction changes for Br > 90. Finally, the effects of El, beta, epsilon, xi, Pr, and Br on the distribution of stress components, velocity, temperature, Nu, and C-D were investigated. Two accurate correlations were proposed for the variations of C-D and Nu against El, which were validated for a wide range of El. (C) 2019 Elsevier B.V. All rights reserved.