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Do you guys think I can analyze the heat in this way: Seperating the heat in the tube into many chunks of heat units ΔV. The volume of each units is the same. Then as the area S is constant. So the length of each unit will be the same Δl.

Here is the hypothesis; if

I. The heat units are all continuous

II. The volume of each units cannot be compressed

Then I will have each unit has the same velocity v0

And other hypothesis, if

in a very short time t, a heat ΔQ(t) transmits into the tube, each part in the tube will obsorb the same amount of heat (ΔL/L)ΔQ(t).

Do you agree with all these hypothesis? If so, I can deduce the Fourier's Law of Heat Conduction. If not, please tell me your thoughts. Thank you!