Prandtl number effects on heat transfer in viscoelastic turbulent channel flow

In viscoelastic turbulent wall-bounded flows, the suppression of near-wall vortical structures due to viscoelastic stress significantly reduces both the frictional drag and heat transfer. To investigate the effect of the Prandtl number ( Pr) on the heat transfer reduction rate (HTR), we conducted a series of direct numerical simulations of passive scalar transport using the finitely extensible nonlinear elastic-Peterlin (FENE-P) model for a viscoelastic turbulent channel flow. Various values of Pr from 0.1 to 5.0 were tested at a frictional Reynolds number of 125. The results revealed that the HTR was almost constant for Pr >= 2.0 at a given drag-reduced flow and was higher than the drag reduction rate, aligning with previous experimental observations. However, in the case of lower- Pr fluids ( Pr <= 0.7), the HTR decreased as Pr decreased. The variation in the Nusselt number ( Nu) for Pr was examined by decomposing Nu into three components: laminar flow contribution, turbulent heat flux contribution, and contribution owing to the deviation in the mean velocity profile from the laminar profile. For lower- Pr fluids ( Pr <= 0.7), the contribution of the wall-normal turbulent heat flux was insufficient to achieve the same HTR as that observed for Pr = 5.0. Despite the reduced wall-normal turbulent heat flux in the viscoelastic flows, the instantaneous flow fields showed a substantial similarity in the turbulent structures of the Reynolds shear stress compared to those of the wall-normal turbulent heat flux, which was maintained at various Pr values. This was also statistically confirmed through the weighted joint probability density function.