Silicon carbide nanowires of diameter D = 20 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 air at 20°C. The exposed silicon carbide fins are L = 500 nm long. The nano-heat sink includes an array of nanofins, and the spacing between two neighboring fins is 30 nm. The water flow velocity in both cases is 10 m/s. Determine the maximum allowable heat rate that can be generated by the electronic device so that its temperature is maintained at Tt _ 85°C for the unfinned and finned packages. Hints: Assume flow over a plate in the unfinned case and cross flow in the nano-finned case. Drawing diagrams of thermal circuit, heat transfer rates or heat fluxes, temperatures, etc. Stating which equations, figures and tables you are using at each step. How many fins are in the nano-finned case? Compute the flow over a plate problem and the cross flow problem. Is it Laminar or turbulent flow in the unfinned problem? Solve the total heat transfer rate for the entire structure. Will the two sides of the package be considered?