## 1 Introduction  
The fluid-dynamics of low-Prandtl-number liquid metals is currently being studied due to an increasing interest in the applications of these fluids in engineering problems. Advanced nuclear reactor designs cooled with liquid metals have been proposed in the Generation IV Forum and some liquid metal fast nuclear reactors have been built and operated [1]. Liquid metal fluid dynamics is also studied in other engineering fields as they are considered possible coolants for new solar power systems [2]. These fluids show low dynamical viscosity with high thermal conductivity and therefore low Prandtl numbers. Two main important coolants for Generation IV nuclear reactors are sodium and lead-bismuth eutectic. The coolant Prandtl number depends on the operational temperature of the reactor; in particular, with increasing temperature the Prandtl number decreases. The Prandtl number of lead-bismuth eutectic is in the range of 0.03-0.01, while sodium has a lower Prandtl with values ranging from 0.01 to 0.005 [3]. Despite the increasing interest in reliable computational tools for these fluids for the study of turbulent heat transfer in complex industrial applications with liquid metals, they are still lacking in commercial codes. The study of reliable and robust computational techniques to deal with this problem is still in the development phase [1; 4; 5; 6; 7; 8]. Due to the complexity of the modeling, different approaches have been proposed by different authors. [PERSON] in his work [1] attempted to model the temperature variance equation for turbulent natural convection; meanwhile, [PERSON] et al. in [4] proposed a modeling of the turbulence Prandtl number based on experimental data in circular tubes. Near-wall modeling and Kays correlation based on Large Eddy Simulations (LES) for forced convection at low Prandtl numbers is described by [PERSON] et al. [5] and [PERSON] et al. in [6]. [PERSON] et al. in [7] presented an overview of different algebraic models for prediction of heat transfer turbulent flow. In [PERSON] et al. [8] a four equation turbulence model is introduced for single rod and rod bundle simulations. Direct numerical simulations are being used to investigate these physical phenomena but an accurate prediction of heat transfer in industrial applications, such as heat exchangers or nuclear reactor pools, cannot rely on this technique due to limitations of the available computational resources [6; 9; 10; 11; 12]. On the other hand, numerical data obtained with Direct Numerical Simulations (DNS) are of strong interest for the validation of turbulence models based on Reynolds averaging Navier-Stokes approach because they can be used to finely tune the turbulence model in the low-Reynolds-number regime. Reynolds Averaged Navier-Stokes (RANS) modeling has been successfully employed in multiple sectors, such as aeronautical, the automotive industry, the nuclear industry and many other fields where DNS is not affordable. In this framework it is very common to assume similarity between the dynamical and thermal turbulent transfer and therefore to define a constant, turbulent Prandtl number as the ratio between the eddy viscosity and eddy thermal diffusivity. For fluids with \(Pr\sim 1\) the turbulent Prandtl number is set to \(Pr_{t}=0.85\)-0.9, but for liquid-metal flows this assumption is known to be invalid [4; 5; 7]. Several solutions have been proposed to deal with this problem. One possible method is to evaluate the turbulent Prandtl number by means of correlations employing global parameters of the flow, such as Reynolds or Peclet numbers. In [PERSON] et al. [4] a constant \(Pr_{t}\) is assumed on the whole domain, case by case, as a function of the Reynolds number. Another possible solution is to define a local turbulent Prandtl number as a function of flow variables, as proposed by [PERSON] [13]. In their work, [PERSON] et al. [5] studied this and other local or global correlations and compared the results obtained in a few test cases.