Discussion on heat transfer correlation in turbulent channel flow imposed wall-normal magnetic field

Heat transfer degradation in high Prandtl number fluid was evaluated via direct numerical simulation (DNS). Target flow fields were fully developed turbulent channel flows imposed a wall-normal magnetic field in the high and low Prandtl number conditions (Pr = 5.25 and 0.025, respectively). Values of the bulk Reynolds number (Re b = 14,000) and the Hartmann number (Ha = 0–32) were set to be equivalent to those of the previous experimental study by Yokomine et al. The numerical results of the Nusselt number for the high Prandtl number fluid were in good agreement with the experimental results by Yokomine et al. However, the magneto-hydrodynamics (MHD) effect on the heat transfer degradation was considerably larger than the empirical correlation proposed by Blum, particularly in the large interaction parameter range. On the other hand, the DNS results for the low Prandtl number fluid were consistent with the empirical correlation proposed by Blum and the experimental results by Gardner and Lykoudis. Therefore, we proposed a new correlation of the MHD heat transfer in high Prandtl number fluid (Pr = 5.25), and suggested that the empirical correlation proposed by Blum could be recommended for low Prandtl number fluid in the large interaction parameter range.