Effect of fluid elasticity and shear thinning on heat transfer from a heated sphere at moderate Reynolds numbers

Abstract

The drag and heat transfer characteristics of an isothermal sphere in a FENE-P-type viscoelastic fluid have been studied in the steady axisymmetric flow regime. The governing equations, namely, mass, momentum, and energy equations, together with FENE-P type viscoelastic constitutive equations, have been solved using the finite volume method based opensource CFD code OpenFOAM over the following ranges of conditions: Reynolds number, 1 ≤ Re ≤ 100 ; Prandtl number, 1 ≤ Pr ≤ 50 ; Weissenberg number, 0 ​ ≤ Wi ≤ 10 and polymer extensibility parameter, 10 ≤ L 2 ≤ 500 for a fixed value of the polymer viscosity ratio of β = 0.5 . At low Reynolds numbers, fluid viscoelasticity causes an upward and downward shifting in the axial velocity profiles with reference to that in a Newtonian fluid along the upstream and downstream axis of the sphere, respectively. However, such a shift progressively diminishes with the increasing Reynolds number. Furthermore, a “velocity overshoot” and/or a “negative wake” is also observed in a viscoelastic polymer solution at low Reynolds numbers, and this is accentuated with the increasing Weissenberg number. The separation of boundary layers is seen to be suppressed with the increasing Weissenberg number. The drag coefficient decreases with the Reynolds number irrespective of the fluid type and the corresponding dependence on the Weissenberg number is found to be non-monotonic depending upon the values of Re and L 2. The average Nusselt number always increases with the increasing values of Re, Pr, and Wi and with the decreasing value of L 2. A limited number of simulations have also been carried out to show the effect of the temperature-dependent viscosity of the fluid on the flow dynamics and heat transfer characteristics. Finally, simple correlations for the drag coefficient and average Nusselt number are presented which not only capture the functional dependence but also can be used for the interpolation of the present results for the intermediate values of the governing parameters in a new application.