The discrete-element model for flows over rough surfaces considers the heat transferred from a rough surface to be the sum of the heat convected from the flat surface and the heat convected from the individual roughness elements to the fluid. In previous discrete-element model development, heat transfer experiments were performed using metallic or high-thermal conductivity roughness elements. Many engineering applications, however, exhibit roughness with low thermal conductivities. In the present study, the discrete element model is adapted to consider the effects of finite thermal conductivity of roughness elements on turbulent convective heat transfer. Initially, the boundary-layer equations are solved while the fin equation is simultaneously integrated so that the full conjugate heat transfer problem is solved. However, a simpler approach using a fin-efficiency is also investigated. The results of the conjugate analysis and the simpler fin-efficiency analysis are compared to experimental measurements for turbulent flows over ordered cone surfaces. Possibilities for extending the fin-efficiency method to randomly-rough surfaces and the experimental measurements required are discussed.

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