A scale analysis of liquid metal natural convection between vertical plates under a transverse magnetic field

Liquid metal natural convection heat transfer under a transverse magnetic field is a fundamental problem in a fusion reactor. Several previous experimental and numerical studies have addressed this problem, however, few studies have focused in the development of correlations giving the heat transfer rate. The most important result in this problem is the existence of a maximum value of the heat transfer rate greater than its value in the absence of the magnetic field. In this paper, we propose to develop a correlation giving the heat transfer rate of the NaK liquid metal through a vertical wall heated by a uniform heat flux and subjected to a transverse magnetic field perpendicular to the thermal gradient. The scale analysis method was used to obtain the general form of the heat transfer rate correlation, while the previous experimental data were used to determine the various parameters and weight coefficients introduced. The results show that the proposed correlation predicts well the heat transfer behavior of the NaK liquid metal in the presence of a transverse magnetic field.