Silicon carbide nanowires of diameter D = 15 nm can be grown onto a solid silicon carbide surface by carefully depositing droplets of catalyst liquid onto a flat silicon carbide substrate. Silicon carbide nanowires grow upward from the deposited drops, and if the drops are deposited in a pattern, an array of nanowire fins can be grown, forming a silicon carbide nano-heat sink. Consider finned and unfinned electronics packages in which an extremely small, 10 µm × 10 µm electronics device is sandwiched between two d = 100- nm-thick silicon carbide sheets. In both cases, the coolant is a dielectric liquid at 20°C. A heat transfer coefficient of h = 1.0 × 105 W/m²K exists on the top and bottom of the unfinned package and on all surfaces of the exposed silicon carbide fins, which are each L = 300 nm long. Each nano-heat sink includes a 250 x 250 array of nanofins. Determine the maximum allowable heat rate that can be generated by the electronic device so that its temperature is maintained at T, < 75°C for (a) the unfinned and (b) the finned packages.