In this paper, an original analytical methodfor determining the evolution of electromagnetic quantities in cylindrical inductor-load systems of arbitrary skin-depth is proposed. This fast and flexible approach aims at facilitating the dimensioning of induction heating facilities. The 1-D induction equation is first analytically solved in the load. The transformer theory is thenapplied, allowing to define the true boundary condition (BC) for the electromagnetic field. The latter issue is then enhanced as a means of highlighting the relevance of the present method when compared with other reference works. The predictions of the analytical approach are then benchmarked with purely numerical results. Finally, a typical application is highlighted, consisting in the optimization of the electrical efficiency of a given induction heating facility.