A method of the analysis of the thermal field dynamics in a core and insulation of a DC lead with convectional heat abstraction

A method of the analysis of dynamics of the thermal field in a DC lead is presented in this article. The cooling of the system is modeled by the convectional boundary condition. Field functions are determined analytically by the method of states superposition and the separation of variables. The coefficients of field functions and eigenvalues of the boundary-initial problem are computed by the numerical method. The coefficients are the solution of the respective systems of equations. Those systems are the result of scalar products of the functions non-orthogonal in the region of the core and insulation. On the other hand, the eigenvalues are determined with the aid of the original algorithm, which, among others, takes advantage of field properties and the method of golden partition. Consequentially, the spatial-temporal distribution of a temperature is computed, as well as the averaged time constant of the system and the admissible long-lasting ampacity. The influence of the heat transfer coefficient and thickness of insulation is discussed. The obtained results have been verified with the aid of a finite element method.