Towards identification of a reliable framework to predict the thermal field in turbulent wall-bounded shear flows

Abstract

Heat transfer modeling plays an integral role in design and optimization of traditional, as well as modern emerging thermal-fluid systems. However, mostly available models, known as eddy diffusivity models, face challenges in prediction of second order statistics such as heat fluxes in homogeneous directions and temperature variance. Additionally, these models are developed targeting fluids with Prandtl (Pr) number around unity and thus, having difficulty to capture thermal fields of working fluids with Pr numbers significantly different than unity at an acceptable level of accuracy. In an attempt to take first step to address the existing shortcomings, this investigation aims to identify a reliable framework to predict the turbulent thermal field of fluids with different Pr numbers (0.025, 0.71 and 10) in wall-bounded shear flows. Towards this, most advanced models, i.e. implicit and explicit algebraic turbulent heat flux models that try to incorporate the anisotropic nature of the turbulent heat flux, have been applied to a turbulent attached boundary layer of various working fluids with significantly different Pr numbers. It turns out that the explicit framework based on the representation theory is potentially capable of dealing with complex turbulent thermal fields and to address shortcomings of currently available models. Moreover, it has been shown that thermal time scale plays an integral role to accurately predict thermal field of fluids with Pr numbers significantly different than unity, as well as high order statistical quantities (e.g. temperature variance) of fluids with Pr numbers around unity.