A large hot surface is positioned L = 0.2 m away from an equally large parallel surface with very low thermal conductivity. Previously. the hot surface was cooled by continuously pumping water along its surface using an 125 W pump. The electricity used to power the pump was priced at 0.39 per kWh. It is now proposed to add an array of equally-spaced fins to the hot surface, with the length of the fins equal to the gap between the two surfaces, such that the tip of each fin is just in contact with the surface with very low thermal conductivity, as shown in the figure. The fins will be manufactured from aluminium, which has a thermal conductivity of k = 180 W/mK. The temperature on the hot surface is 323 K, and the temperature of the surrounding air is 298 K. The heat transfer coefficient between the fins and the air is h = 20 W/mK. Surface with very low thermal conductivity Fins Hot surface Lm a) By considering maximum effectiveness, demonstrate whether circular- or square-cross section fins should be used. Assume that the cross sectional area is A = 0.0004 m for whichever geometry is chosen. Type your chosen cross section here (either circular or a) By considering maximum effectiveness, demonstrate whether circular- or square-cross section fins should be used. Assume that the cross sectional area is Ac = 0.0004 m for whichever geometry is chosen. Type your chosen cross section here (either circular or square): b) What is the efficiency of a single fin with the cross section chosen in part a)? Give your answer to the nearest whole number as a percentage (e.g. 54.32% would be given as 54): c) To maintain a constant temperature at the surface, 2500 W of heat must be removed by the fins (as this was previously removed by the water). Using the cross section identified in part a), how many fins will be required? Give your answer as a whole number: d) Given that aluminium costs 0.70 per kg, and its density is 2710 kg/m, how long will it take for the extra material cost to be paid back by the reduced operating cost when the fins replace the pumped water system? Give your answer to the nearest whole number of days: