Theoretical study in two dimensions of the energy transfer between an electric arc and an anode material

In many thermal plasma applications, the knowledge and control of energy transfer is essential. Numerical models taking the interaction between plasma and material into account are being developed but the results need to be validated by experiment. Before considering experimental measurements to deduce the heat transferred to a material, we develop a theoretical approach studying the ability of inverse methods to reconstruct the temperature field and the heat flux profile applied at the surface, starting from temperature values in the material. After a study of the literature, the conjugate gradient method and the least squares methods were chosen for our configuration. Numerous parametric tests were performed (position, number of temperature points and the introduction of noise on data) to compare the two methods and to study their suitability. In the case of heat fluxes of around 107-108W m-2 and iron materials, the Tikhonov method showed its limitations but the conjugate gradient method demonstrated its suitability for implementation in our experimental setup to reconstruct the heat flux and the temperature field that could be obtained by the interaction of an electric arc with a material in an axisymmetrical configuration