Abstract
In this paper, a study of the elemental construct of an I-shaped fin cooling a heat generating plate is conducted in the framework of the constructal design method. Using the minimization of the maximum excess of temperature as an objective and considering that heat is generated in the conductive strip within a certain surface and with a different amplitude from the plate, the constructal design method permits to obtain a new optimal shape ratio (more general than the optimums found in the literature considering no-generation in the conductive strip or heat generated with the same amplitude in the two materials). Then, the thermal model used until here in stationary state (hypotheses on heat diffusion) is extended to take into account the time. The analytical solution obtained (verified numerically) is compared to classical heat diffusion through an engineering application (cooling an electronic device) where it keeps a good precision for times larger than 1% of the stationary time.
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