Direct numerical simulation of one-sided forced thermal convection in square ducts*

We perform direct numerical simulations (DNS) of forced thermal convection within one-sided heated square ducts up to friction Reynolds number 2000, comparing the global heat transfer to the academic scenario of uniformly heated walls. Similarly to the case of plane channel flow, and in agreement with early experiments, we find a significant reduction of global heat transfer compared to the uniformly heated case. The reduction of global heat transfer depends on the Reynolds number, and levels off to approximately 10%, at unit Prandtl number. The global heat transfer in square ducts closely parallels that in plane channel flow under similar boundary conditions when we match to the bulk Reynolds number based on the effective diameter. Our results illustrate that the use of traditional engineering formulas, devised for uniform heating scenarios, could potentially introduce substantial uncertainty into global heat transfer coefficient predictions. Consequently, it is essential to consider heat distribution when estimating global heat transfer.