The Impact of Surface Area on the Radiative Thermal Behavior of Embedded Systems

A new global analytical model of the heat dissipation process that occurs in passively-cooled embedded systems is introduced, and we explicit under what circumstances the traditional assumption that exponential cooling laws apply in such context is valid. Since the power consumption and reliability of microprocessors are highly dependent on temperature, management units must be able to rely upon accurate thermal models. Exponential cooling models are justified for actively-cooled microprocessors. For passively cooled processors however, as frequently found in embedded systems such as mobile devices, an exponential law may not be theoretically justified. Here, we analyzed the tractability of the cooling law for a passively cooled body, subject to radiative and convective cooling. Focusing then on embedded microprocessors, we compare the performance difference between our new passive cooling law and the conventionally-used exponential one. We show that, for isothermal cooling surfaces of the order of 1 dm2 or greater, the radiative cooling effect may become comparable to the convective cooling one. Otherwise for surfaces below 1 dm2, we show that the differences between the exact solution and the exponential cooling law are negligible. In the absence of accurate temperature measurements, an exponential cooling law is shown to be accurate enough for small-sized SoC systems that require low processing overhead.