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 un finned electronics packages in which an extremely small 10μm X 10μm 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 X 105 W/m2 ∙ K exists on the top and bottom of the un-finned package and on all surfaces of the exposed silicon carbide fins, which are each L = 300 nm long. Each nano-heat sink includes a 200 X 200 array of nano-fins. Determine the maximum allowable heat rate that can be generated by the electronic device so that its temperature is maintained at T.