The influence of frontal solidity on fully rough heat transfer modeled through an exposed and sheltered flow dichotomy

The challenge of predicting rough-wall heat transfer is embodied by the many factors which must be considered: the working fluid dependence (Prandtl number Pr), the flow regime (roughness Reynolds number k⁺), and further parameters required to characterize any given roughness. Here, we will focus on one particular geometric parameter in the frontal solidity, Λ. With direct numerical simulation data, we will show that in the fully rough regime (high-k⁺), the local heat transfer can be meaningfully decomposed into two distinct regions: exposed regions following a Reynolds Analogy behaviour and sheltered regions where the heat transfer is spatially-uniform. The total heat transfer follows as a sum of these mechanisms, with their contributions weighted by Λ. We will present a model for the total heat transfer by considering different heat transfer laws in exposed and sheltered regions.