A comprehensive assessment of the Reynolds Analogy in predicting heat transfer in turbulent wall-bounded shear flows

Abstract

Heat transfer modeling plays a major role in design and optimization of modern and efficient thermal-fluid systems. However, currently available models suffer from a fundamental shortcoming: their development is based on the general notion that accurate prediction of the flow field will guarantee an appropriate prediction of the thermal field, known as the Reynolds Analogy. This investigation presents a comprehensive assessment of the capability of the Reynolds Analogy in predicting turbulent heat transfer when applied to turbulent shear flows of fluids with different Prandtl numbers. It turns out that the Reynolds Analogy is able to provide acceptable results for first order statistics only when fluids with Prandtl number close to unity are considered. Further, it is shown that unsteady simulations could provide acceptable results on second order statistics concerning fluids with different Prandtl numbers, if appropriate grid design/resolution is provided that allows to resolve essential dynamics of the thermal field. However, accurate prediction of higher order statistics close to solid surface requires more advanced heat transfer models that can provide accurate information on thermal time scales, in case the grid is too coarse to support accurate resolving of the essential thermal dynamics in these regions.