Big_T
Posts: 3089
Joined: 6/7/2007
From: Milwakuee, WI
Status: offline
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Ok, it's been 5 years since I've done this and I don't do a lot of hand HT calcs, especially using Fourier series so you'll have to bear with me for a moment. You'r just talking aout B) now, right? Assuming you are: the heat transfer on the sides is not 0, the temperature on the sides is 0. A perfectly insulated edge should have a heat flux of 0, so if it were saying that the heat transfer is 0 on an edge, that's the same as saying it is perfectly insulated. If we were dealing with transient solutions it would be difficult (as well as being a good enough reason to revolt against your professor) but since it's a steady state solution we are dealing with it's simply looking at what the final temperature would be. There will be heat transfer across the vertical sides in a transient solutions but at steady state it will be a simple final solution because the plate will equalize. A way to think of this is to say you've got a square steel plate and you heat it up to 300 degrees. Then you take the steel plate out and put it in a frame which is lined on the horizontal sides with bricks (perfectly insulated) and on the vertical sides with a cooling edge at 0 degrees. What's going to happen? It's going to start cooling the sides quickly and you'll get temperature gradients throughout the plate. Eventually the plate will even out at 0 degrees (though it will take awhile) Now, think of if one side was cooled at 0 degrees and the other side was 10 degrees. You'd end up with temperature gradients (isotherms) throughout the plate.
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