Analysis of thin film liquid metal protection of fusion reactor plasma contact surfaces

Presented in this work is a method of analyzing the heat transfer characteristics and flow parameters of a thin films of liquid metal flowing on a substrate in the presence of a strong magnetic field, and exposed to a large, one-sided heat flux. This method can then be applied to the problem of determining the effectiveness and flow parameter ranges of a thin film liquid metal used for the protection of plasma contact surfaces in fusion reactors. Previous work in the area of the heating of film liquid metal surfaces as applied to fusion has been confined to the assumption of a constant heat flux incident on the free surface. This treatment can help to give an idea of the magnitude of the removable heat flux as well as to establish a basis for a heat removal comparison of different liquid metals; but falls short when analysis of a real, spatially varying heat flux is required for determining the maximum film temperature and needed film velocity. For this reason, a new method involving the solution of the two-dimensional energy equation with an arbitrary, space-varying heat flux boundary condition at the free surface is developed. Application of this approach to several fusion relevant situations yields the temperature at any point in the film flow and can be used to determine the velocity needed to keep the maximum film temperature below whatever film temperature limit is imposed. Given the required velocity, it then becomes necessary to determine the behavior of the film at this speed. Previous efforts to do this have involved the development of one-dimensional models for the film height, derived from the basic set of magnetohydrodynamic equations and a variety of simplifications and assumptions. This work re-derives these models, while correcting small errors and using a modified set of assumptions that are more applicable to fusion situations