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Convective heat transfer in laminar conditions is studied numerically for a Prandtl number Pr = 0.025, representative of liquid lead–bismuth eutectic (LBE). The geometry investigated is a channel with a periodic series of shallow cavities. Finite-volume simulations are carried out on structured orthogonal curvilinear grids, for ten values of the Reynolds number based on the hydraulic diameter between Rem = 24.9 and Rem = 2260. Flow separation and reattachment are observed also at very low Reynolds numbers and wall friction is found to be remarkably unequal at the two walls. In almost all cases investigated, heat transfer rates are smaller than the corresponding flat channel values. Low-Prandtl number heat transfer rates, investigated by comparison with Pr = 0.71 results, are large only for uniform wall temperature and very low Re. Influence of flow separation on local heat transfer rates is discussed, together with the effect of different thermal boundary conditions. Dependency of heat transfer performance on the cavity geometry is also considered.

In the frame of the future generation of nuclear reactors, liquid metals are foreseen to be used as a primary coolant. Liquid metals are characterized by a very low Prandtl number due to their very high heat diffusivity. As such, they do not meet the so-called Reynolds analogy which assumes a complete similarity between the momentum and the thermal boundary layers via the use of the turbulent Prandtl number. Particularly, in the case of industrial fluid-dynamic calculations where a resolved computation near walls could be extremely time consuming and could need very large computational resources, the use of the classical wall function approach could lead to an inaccurate description of the temperature profile close to the wall. The first aim of the present study is to investigate the ability of a well- established commercial code (ANSYS FLUENT v.14) to deal with this issue, validating a suitable expression for the turbulent Prandtl number. Moreover, a thermal wall-function developed at Universite Catholique de Louvain has been implemented in FLUENT and validated, overcoming the limits of the solver to define it directly. Both the resolved and unresolved approaches have been carried out for a channel flow case and assessed against available direct numerical and large eddy simulations. A comparison between the numerically evaluated Nusselt number and the main correlations available in the literature has been also carried out. Finally, an application of the proposed methodology to a typical sub-channel case has been performed, comparing the results with literature correlations for tube banks.