Joule heating in magnetohydrodynamic flows in channels with thin conducting walls

Joule heating in liquid metal magnetohydrodynamic flows is investigated with reference to self-cooled liquid metal blankets for tokamaks. Pressure-driven flow of an electrically conducting fluid confined between two parallel, infinite walls with a transverse magnetic field is studied. The walls are electrically conducting, which implies strong currents flowing within the thin conducting walls. The problem is solved both analytically and numerically.It is shown that the Joule heat cannot be neglected in certain range of parameters relevant to fusion blanket applications. The magnitude of the Joule heat released inside the channel and the walls depends on the thermal conductivity of the outside surface of the channel walls. For thermally conducting outside surface of the walls the Joule heat can become significant for high values of the Hartmann number and moderate average velocity. The effect is even more pronounced for thermally insulating outside surface of the walls. For example, for lead–lithium flow with stainless steel walls the temperature increase along the flow exceeds 200 °C over the length of the blanket, which is almost three times higher than that for thermally conducting outside surface of the walls.The main reason for such a strong rise in temperature is the heat released inside the walls. The heat produced in the fluid region is quickly convected towards the exit from the channel. The heat released inside the walls can only leave the domain by diffusion into the fluid region and thus is accumulated along the channel length.