Direct numerical simulation of forced thermal convection in asymmetrically heated channels

We carry out direct numerical simulation (DNS) of turbulent channel flows at different Prandtl numbers and up to friction Reynolds number Re_τ≈2000, considering flow cases with both symmetric and asymmetric heating[1-2]. The latter configuration has been studied considerably less, although it is certainly the most relevant for engineering applications, where heating is often concentrated on one wall. We show that one-sided heating modifies the temperature fluctuations in the outer layer, where we observe large-scale eddies extending well beyond the channel half height. We show that also in the case of one-sided heating the temperature profile exhibits a logarithmic layer and a wake region, which can be approximated using a parabolic profile. We use these universal features of turbulence to derive analytical approximations for the Stanton number, and to quantify the thermal efficiency of one-sided-heated channels compared the idealized symmetric cases. We find that the thermal efficiency is reduced by up to 30% at low Prandtl number, whereas the increasing relevance of turbulent convection tends to level off the differences at higher Prandtl number, with a heat transfer reduction of about 10% at Pr=4.