Spatial frequency domain heat transfer analysis of hot spot spreading in convectively cooled microprocessors

Spatial frequency domain (SFD) analyses of heat transfer along with the spatially-resolved imaging of microprocessor power (SIMP) method have provided a deeper understanding of the thermal behavior of microprocessors. In the present work, the thermal transfer function of a convectively cooled chip is written as a summation of functions with known Hankel transform pairs. Subsequently, the impulse response (obtained by deriving the inverse Hankel transform of the transfer function) is used to perform two-dimensional convolutions in the space domain. As expected, the thermal transfer function, which basically has the characteristics of a low pass filter, preserves the inputs with larger dimensions, whereas inputs with smaller sizes tend to expand. Interestingly enough, the expansion and spreading are not linearly related to the heat source size, and the system selectively spreads certain sizes more than others.