Assessment of thermo-fluid analogies for different flow configurations: the effect of Prandtl number, and laminar-to-turbulent flow regimes

The differential equations of momentum and heat transfer are similar to each other based on some assumptions, leading to exact analogous equations. These analogies have since been the focus of attention and their applicability is explored in many fields and flow types. In some cases, these analogies hold valid even if the theoretical foundation is not available for such conditions. The Reynolds and Chilton-Colburn analogy are the focus of the current work, with four types of flow situations including, Couette flow, tube flow, parallel plate and flow over a flat surface. The numerical results show the best match for parallel flow and flat plate, while Couette flow resulted in large differences (by a factor up to 3.3).