Universal thermal profiles with polynomial thermal diffusivity in a channel flow

Fluids used in heat transfer applications range in a wide spectrum of Prandtl numbers. An aspect that is commonly neglected is the influence of variable thermal diffusivity in turbulent heat transfer. A mathematical model was developed in the past few years [1, 2] to address the influence of the variable thermal diffusivity on the turbulent heat transfer. In this work we explore the influence of the friction Reynolds number Reτ, the molecular Prandtl number Pr and the coefficients λi+ of the temperature dependent thermal diffusivity, up to the fourth-order, to the Universal Profiles in a channel flow. This choice minimizes the influence of the boundary and initial conditions. The numerical simulations in the limit of constant thermal diffusivity are validated against literature DNS data. The results show that the influence of the friction Reynolds number is limited, while high molecular Prandtl numbers increase the fluctuating thermal diffusivity heat flux. The factor that influences the solution the most is the thermal diffusivity coefficients, showing that, in certain conditions, the fluctuating thermal diffusivity heat flux is non-negligible even for low Prandtl numbers. The results show that the terms introduced by the model proposed in [1, 2] are non-negligible when the thermal diffusivity in the boundary layer doubles compared to its bulk value. It is suggested that the model presented in [1, 2] could be particularly suitable in cryogenic applications.