Thermal, Mechanical, and Diffusion Processes in Conducting Solids Placed in External Magnetic Fields Periodic in Time

Abstract

We propose a procedure of quantitative description of the correlated processes of deformation and heat, mass, and electric-charge transfer in conducting solids under the action of external magnetic fields periodic in time. By the methods of similarity theory and dimensional analysis, the set of equations of magnetothermomechanical diffusion is reduced to the dimensionless form. We perform the quantitative analysis of the characteristics of dimensionless criteria for the diffusion of carbon into iron. In our model, we neglect the effects for which typical dimensionless parameters are much smaller than one and deduce a simplified set of equations for the electromagnetic field, temperature, and mechanical stresses in conducting ferromagnetic solids.