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 = 8 mm, and width W = 24 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[infinity] = Tsur = 30°C. The surface has an emissivity of ε = 0.9, and the convection coefficient is h = 8 W/m^2 · K. The case is completely enclosed such that heat transfer may be assumed to occur exclusively through the base plate. Requried:
a. If the air-filled aluminum-to-aluminum interface is characterized by an area of Ac = 2 × 10^−4 m^2 and a roughness of 10 μm, what is the maximum allowable power dissipation if the surface temperature of the case, Ts, 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 varying the coefficient over the range 4 ≤ h ≤ 200 W/m^2K.