00:01
Hi there, so for this problem, we are told that a pin fin of uniform cross -septional area is fabricated of an aluminum alloy with a thermal conductivity that is given, and that thermal conductivity that we're going to express with the letter k is equal to 160 watts per meter per kelvin.
00:29
And the fin diameter is also given, let's call this diameter.
00:33
Capital d that is equal to 4 millimeters, 30 meters is equal to 0 .004 meters.
00:45
And the fin is supposed to a combative condition, characterized by the constant age that is equal to 220 watts per meter square per kelvin.
01:07
With that said, it is reported that the fin efficiency is also given, and that efficiency is equal to 0 .65.
01:22
So the question for part a of this problem is about what is the length of the fin.
01:32
Now, for a circular fin, like in this case, the effective mass is equal to the square root of 4 times the convective coefficient divided by the thermal conductivity times the diameter.
01:57
So we can obtain this value by just substituting the values in here.
02:02
So we will have the square root of 4 times 220.
02:10
This divided by the thermal conductivity 160 times the diameter that is 0 .00.
02:19
04, which is square root of all of this.
02:22
So from this we obtain a value of 37 .1.
02:31
Now we use the equation for the efficiency of the circular fin to find out the corrected length of the film that we're going to call lc.
02:46
So that efficiency is defined as the tangent of, well, the hyperbolic tangent of h.
03:00
Times the effective mass times the length lc.
03:05
This divided by the mass times the length lc.
03:09
We can cancel the masses...