My hypothesis is to use two different stable heat sources with different tempreature T1 and T2 (T1>T2) transmits the heat . Then I let the distance between this two heat sourse filled with idea gas or ideal metal in a tube. So if the distance is L, the heat capacity is Cv (Constant). So the temperature at r. (r is the distance to heat source T2 0<r<L). Then when the system balances, we have the temperature T(r)=T1+(T2-T1)r/L. That is the fourier's law form. I will tell you my way to deduce this formula in details if you are interested in this research. 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!