You are asked to design metal fins for the radiative cooling of a thermal device. The device has a cylindrical shape as in Figure (a) and generates heat with a power of 1 kW, which diffuses to the surface and gets emitted as thermal radiation. Assume that the material used for the surface is a rough metal with high thermal conductivity (so its temperature is uniform over the entire surface of the cylinder and fins) and the emissivity is 1. Assume only radiative heat transfer (no conduction or convection; this would apply for example to a thermoelectric device used by NASA in space). Also, assume that heat is emitted from the side and top surface of the cylinder only (but not the bottom flat surface of the cylinder) as well as from the flat surfaces of the fins, and that any heat emitted by one of the surfaces does not get reabsorbed by any other (this is a simplification for the purposes of this problem, but you can account for it using software in an actual situation).

(a) 0.5 m WW 0.5 m (b) 0.5 m W