Two very long parallel cylindrical channles are drilled through a very large block of material. The block is so large, that it can be considered infinitely large.
http://i24.tinypic.com/2mhu73s.jpg
The diameter of the channels is 16cm, and distance between theier centers is 20cm. One cylinder contains cold +10C water, and the other contains hot +50C water. Thermal conductivity of the material is 10 W/cm/C.
How much heat flows from hot to cold water per 1cm length?
2007-10-05 05:32:08 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Physics
It is true that thermal conductivity is exactly equivalent to electrostatics.
But the main difficulty is how to equalize temperature (or voltage if you wish) on the surface of the pipes (or cylidrical conductors).
One charged cylindrical conductor indeed creates field 1/r. But when you bring another charged cylindrical conductor into the vicinity, the latter will destroy equipotentialty on the surface of the former. The charges will have redistribure on the surface, and the field of each cylindrical conductor will be no longer symmetric 1/r.
2007-10-12 06:53:14 · update #1
I believe this problem refers to the fact that heat transfer equation in stationary mode is similart to electrostatic equations, so you can consider your cylinders as long charged wires. For them using Gauss' law you can find that electric field depends as 1/r from the distance to the center of wire. The surfaces of equal temperature would be like the surfaces of equal potential and the heat flux would be similar to electric field flux.
2007-10-11 12:12:50 · answer #1 · answered by Alexey V 5 · 0⤊ 0⤋
If this were a really hard problem, they wouldn't have given it to you as homework. The real question is when will YOU stop to ask other people to do YOUR homework for you and learn how to solve close to trivial problems given to YOU as a way to improve YOUR skills?
2007-10-05 06:25:04 · answer #2 · answered by Anonymous · 0⤊ 4⤋