Hello.. The query is regarding thermal conduction of heat from a solid body: Suppose we have a long metallic rod which is insulated on the curved surface and one of the bases. If we supply Q amount of Heat for a small time to the rod from the non-insulated end, initially the temperature of the end in touch with the sources rises and then due to temperature difference in the rod the heat flows. Since the amount of heat provided is fixed and is cut-off after a while, then the rod tends to attain the uniform spread of heat all over the space, tending towards the spreading of energy (hence rise in entropy.) Now if I supply heat continuously to the rod at one end, then since the rod doesn’t get the opportunity to tend towards distributing the energy uniformly, there should be a temperature difference between the end in touch with source and the one farthest away from it. (Please correct me if I have made any conceptual error). So the rod as a system is unable to tend towards spreading the energy maximum, the entropy is not rising to its maximum ever in this situation. That means, as long as the rod is supplied with heat the temperature should rise, but in practise a steady state is achieved. How does that happen? One more thing, I have read at a few places that conduction in metals is significantly because of the free electrons, and very less due to the vibration in the lattice structure. Reading this I thought, may be the situation I am talking about is because of this fact. The steady state might be reached because the energy of vibration the particular solid can bear (being in the same phase) has a upper limit, after this is reached all the energy is transferred. If now the other base of the rod is brought in contact with say flowing water, then after the steady state is reached all the heat supplied to the rod is given away by it to the water (the rate of flow of water should be less than that of Heat). Is this correct? I would wish to know details of how the conduction actually occurs in the three situations at the atomic or sub atomic level.