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

4. How big is a nacelle?

5. Resolution of the problem 1.43 (1/2)
The mechanical energy dissipated in the gear box and the electrical 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.

6. Heat produced in the generator and in the gear box

7. 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

8. Comments to the result
393K=120 C 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.

9. 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:

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

13. In the resolution the surface area should be twice the value used
In the resolution the surface area should be twice the value used. The plate has 2 surfaces!!!

15. In the balance below, the plate surface is missing: 2*0.3*0.3 m2