In order to augment the rate of cooling of a device, a pin fin of 2.5mm diameter is attached to its casting. The wall of the casting has a temperature of 95°C, whereas it has a temperature difference of 70°C with the surrounding air. Primarily, the heat transfer occurs through natural convection with a convection coefficient of 10 W/m^2.°C.
1) What is the heat loss if the fin is infinitely long?
2) What is the heat loss if the fin is 25mm long and convection process at 113°C occurs with the same convection coefficient as described earlier?
3) How long should the fin be to justify the assumption of its infinite length with a 5% error margin?