Compact thermal modeling methodology for predicting skin temperature of passively cooled devices

Compact thermal modeling of microelectronic systems has recently attracted considerable attention. The present work aims at developing resistor-capacitor (RC) thermal models for predicting time-dependent surface temperature of a passively cooled device. The developed models mimic typical fanless systems cooled by dissipating heat to the surroundings through the enclosure back case by natural convection and radiation. In order to establish a baseline for checking the accuracy of the compact thermal model, the same problem was modeled using three-dimensional, transient, Navier-Stokes equations that were solved numerically by computational fluid dynamics (CFD) code. For constructing Foster RC-network ladders and to find best-fit thermal constants, temperature step responses of the hot-spot were obtained by applying known power pulses on the discrete heat source. Special attention was paid to the characteristics of the RC-network ladders for obtaining a reasonably accurate numerical scheme for real-time calculation of hot-spot surface temperature. In the present study it is demonstrated that the thermal constants (R, τ) are strong functions of the input power. An alternative usage of formulation for multi-ladder Foster RC-network, incorporating time-dependent thermal constants is show-cased. The suggested methodology can be used for non-linear problems involving time- and power-dependent boundary conditions.