The cross-section of prefabricated metallic beams is constant along the path they move. This feature allows solving analytically the temperature field problem by applying the method of spatial eigenfunctions series decomposition in the cross-section. The second order differential equations of the series’ terms can be solved analytically. A Picard- Banach iterative technique with a very fast convergence rate is proposed for solving the eigenvalues problem. The method has a greater efficiency in terms of accuracy and execution times than numerical methods, such that based on the finite element method. It can be shown that when the speed of moving beam is sufficiently small the distribution of the field in the cross-section is almost uniform. For this case a simple and fast procedure which allows the computation of the average temperature variation along the beam is proposed.

Keywords: Analytical method, Space eigenfunctions expansion, Eddy current continuous flow heating