Consider a power transistor encapsulated in an aluminum case that is attached at its base to a square aluminum plate of thermal conductivity k = 240 W/m ∙ K. thickness L = 6 mm, and width W = 20 mm. The case is joined to the plate by screws that maintain a contact pressure of 1 bar, and the back surface of the plate transfers heat by natural convection and radiation to ambient air and large surroundings at T_∞ = T_sur = 25°C. The surface has an emissivity of e = 0.9, and the convection coefficient is h = 4 W/m² ∙ K. The case is completely enclosed such that heat transfer may be assumed to occur exclusively through the base plate.

(a) If the air-filled aluminum-to-aluminum interface is characterized by an area of Ac = 2 X 10^-4 m² and a roughness of 10μm, what is the maximum allowable power dissipation if the surface temperature of the case, T_s.c, is not to exceed 85°C?

(b) The convection coefficient may be increased by subjecting the plate surface to a forced flow of air. Explore the effect of increasing the coefficient over the range 4 < h < 200 W/m² ∙ K.

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Transistor case Base plate, (k, e) elec Interface, A, Enclosure 11 Air L.