Exercises. Introduction to Fins Lecture 6 Exercises. Introduction to Fins

How big is a nacelle?

Resolution of the problem 1.43 (1/2) The mechanical energy dissipated in the gear box and the lectrical generator is transformed into heat. This heat is transferred to the nacelle and this looses it to the atmosphere by convection and radiation. The gear box and the generator loose the heat to the nacelle also by radiation and convection. The temperature inside the nacelle is assumed to be equal to its outside temperature. This is a reasonable assumption if the walls are thin and especially if they are metallic. The temperatures will depend on the heat fluxes and on the atmospheric and sky temperatures (25 and 20 Celsius respectively.

Heat produced in the generator and in the gear box

Temperature of the nacelle surface Using an iterative procedure, starting by assuming as a first guess that: i.e. that there is no radiation One would get after 4 iterations 393K

Comments to the result 404K=131C is two high. This means that the system should be refrigerated using forced convection… Doing a similar calculation one would compute the temperature of the generator and gear box. After some trial and error iterations one gets T=785, that again is too high and would require forced convection to refrigerate the gear box.

Heat is exchanged by convection. The heat flux is: The heat flux is the same in both experiments because it is the same geometry and temperatures and thus convection is the same. As a consequence:

Problem 1.62 The heat capacity is smaller. This is why a heavier sphere has been cooled faster.