Localized heating can be encountered in the operation of transistors, light-emitting diodes, and some thermal spectroscopy techniques. Diffusive analytical and numerical thermal models are popularly used to characterize the thermal resistance of such problems. However, when there is localized heating comparable to the size of the mean free path of the energy carriers ballistic thermal transport, which causes additional thermal resistance is observed. The major objective of this study is to find a relation to describe the thermal resistances caused by the ballistic effects in problems with localized heating. Models based on the solution of the Fourier heat diffusion equation and the gray phonon Boltzmann Transport Equation (BTE) are solved simultaneously for to find this relation. It is observed that although phonon MFP and the power linearly effect the ballistic thermal resistance the effect of geometrical variables is more complicated and needs further analysis.

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