Cauer Ladder Inspired Kron–Branin Modeling of Thermal 1-D Diffusion

This brief introduces an innovative unidimensional thermal propagation modeling. It consists in thermal diffusion on conductor bulk structure based on the Kron-Branin (KB) formalism. The proposed KB model is inspired from the transmission line approach by considering the bulk material thermal resistance and capacitance. The KB-based equivalent graph topology of the heated structure is elaborated. The thermal transfer function (TTF) is established from the graph analytical abstraction. The TTF enables to determine the transient and frequency-dependent temperature diffusion along the structure. The KB model effectiveness is illustrated with both frequency and time-domain analyses. Proof-of-concept constituted by copper-based bulk material is considered. The TTF from KB, finite-element-method and Cauer models are compared. With computation from dc to 100 Hz, it was shown that the frequency domain magnitude and phase are in good correction. In addition, the calculated and simulated transient heat flows along the considered structure are in good agreement by considering 120-ms duration pulse width temperature source.