Contribution of turbulent heat flux to the heat transfer reduction in viscoelastic channel flows

In viscoelastic turbulent channel flows, the suppression of near-wall vortical structures caused by viscoelastic stress leads to a significant reduction in both frictional drag and heat transfer. Previous experiments for high Prandtl number (Pr) fluids reported that the heat transfer reduction rate (HTR) is higher than the drag reduction rate and nearly independent of Pr. However, since the contribution of turbulent heat flux to the total heat flux varies with Pr, HTR related to the decrease in turbulent heat flux may also vary. To investigate the effect of the Prandtl number on HTR, we conducted a series of DNS using the FENE-P model for viscoelastic turbulent channel flow. Various Pr values from 0.1 to 5 were tested at a Re_τ = 125. The results revealed that high Pr fluids (Pr ≥ 2.0) exhibited a higher HTR than the drag reduction rate, aligning with previous experimental observations. However, in the case of low Pr fluids (Pr ≤ 0.7), HTR decreased as the Prandtl number decreased. To understand the decrease in HTR for low Pr fluids, we analyzed the Nusselt number by decomposing it into three components: laminar flow contribution, turbulent heat flux contribution, and contribution due to mean velocity deviation. Our findings demonstrated that at low Pr cases, the contribution of turbulent heat flux was insufficient to achieve the same level of HTR as observed in high Pr fluids. This discrepancy prevented an equivalent reduction in HTR for low Pr fluids.