A critical re-examination of Reynolds analogy for micro-convective flow

Abstract

The present research numerically investigates the validity of the Reynolds analogy for micro-convective water flow between Stanton number (St) and Fanning friction factor (ff), taking into account combined fluid properties variations such as temperature-dependent density, viscosity, and thermal conductivity. The Reynolds analogy is suggested to be valid when St increases for thermophysical fluid properties (TFP) with a decrease in ff. This analogy, therefore, helps to find the flow regime that increases heat transfer while shear stress decreases for TFP. Hence, the Reynolds analogy for TFP helps to design and improve the performance of the different devices, including micro-scale heat exchangers for electronics cooling, internal cooling passages of turbine airfoils, and many biomedical devices. Three modified non-dimensional parameters (ΠSρT, ΠSμT, and ΠSkT) appear from the non-dimensionalization of the governing conservation equations. Using dimensional analysis, the dependence of the friction factor on these parameters is examined.