A method to calculate mixed MHD convention in a vertical channel

A method is proposed for the numerical simulation of heat transfer in a liquid metal flow in a vertical channel with consideration of the effects of a coplanar magnetic field and natural convection. It is demonstrated that, for a downward flow in a heated rectangular channel with an aspect ratio of $3 : 1$, the counteraction of natural convection induces strong velocity and temperature fluctuations that can be taken into account with the proposed method. The first stage of the development of a modeling procedure deals with a numerical solution to a simplified, nonstationary 2D problem of a downward flow in a flat, slot-like channel with uniform heating of one or two walls. At the second stage, the predicted characteristics of the nonstationary 2D flow are used to calculate the averaged characteristics of a 3D flow. The numerical results are verified against experimental data obtained under conditions similar to those used in the calculations.