Turbulent Heat Transfer over roughness: a comprehensive review of theories and turbulent flow structure

Turbulent heat transfer over rough surfaces is crucial in natural and industrial processes, yet it has received less attention than that of momentum transfer. Recently, research in this field is rapidly growing, driven by advancements in computational methods, the role of surface roughness in meteorology, and the growing use of Additive Manufacturing technologies for energy and thermal management systems that inherently create rough surfaces. Despite these advances, a comprehensive understanding of turbulent heat transfer over rough surfaces, along with reliable predictive models applicable across various fields and roughness topologies remains lacking. The present paper reviews the key experimental and numerical studies to explore the mechanisms governing turbulent heat transfer over rough surfaces. It aims to guide future research and provide a solid foundation for understanding rough-wall turbulent heat transfer in various applications, including aerodynamics, meteorology, aerospace, and thermal management systems. By comparing with smooth-wall flows, the paper highlights how surface roughness affects turbulence structures and the thermal boundary layer. Existing models and scaling laws for heat transfer are critically evaluated, with attention to their applicability across different roughness types and flow conditions. The review also examines the analogy between heat and momentum transfer, the impact of roughness on thermal efficiency, and higher-order turbulent statistics. The literature shows that surface roughness breaks the Reynolds analogy, where any rise in Stanton number (St) is paired with a relatively larger increase in skin friction coefficient (Cf). As roughness Reynolds number (ks+) grows, the temperature shift (ΔΘ+), which reflects heat transfer due to roughness, tends to flatten. This behaviour suggests a potential asymptotic thermally fully rough regime that is distinct from the velocity field's behaviour. However, the limited range of Reynolds (Re) and Prandtl (Pr) numbers achievable in numerical simulations allows only speculative conclusions about this asymptotic behaviour. Furthermore, the potential for a reduction in ΔΘ+ at high ks+ values, possibly even becoming negative, remains feasible. The available heat transfer models do not account for either ΔΘ+ trend, highlighting the need for a new theory or a revision of traditional models. It is hypothesised that roughness enhances heat transfer by channelling energy toward colder, high-velocity regions, indicating the importance of roughness thermal conductivity. It is suggested that a universal rough-wall heat transfer theory should incorporate factors including roughness topology, roughness thermal conductivity, ks+, and Pr. In addition to expanding the range of Re and Pr, a systematic examination of various roughness types and topologies is necessary, as the temperature remains sensitive to specific geometric details.