In heat transfer across a rod, why actually steady state occur?
why temperature of sections of rod don't further increase as heat is even flowing through them and as whole rod is of same material then why the one section of rod absorbs more heat while other sections of same rod absorb less heat?
Kindly answer my question in terms of physical meaning not using equations , as equations also have some physical explanations and meanings.
The steady state is reached when the rate at which heat is entering the rod is exactly equal to the rate at which heat is leaving the rod. The temperature of the rod is independent of the rate at which heat is flowing through the rod.
Think of it like a bucket with holes in it that is being filled from a tap. Once the rate at which water leaves the bucket equals the rate at which water enters the bucket, the height of the water in the bucket will remain the same - this is the steady state. If the bucket has many holes then height of the water in the steady state may be very low. If the bucket has only a few holes then the height of the water in the steady state will be higher - the bucket can hold more water if it is less leaky.
You also ask how different parts of the rod can have different steady state temperatures. Well, you can think of the rod as being made up of lots of little rods placed end to end. The steady state temperature of each little rod will depend on the temperatures of the rods on either side of it, which need not be the same. So each little piece of the rod may have a different steady state temperature, even though they all have the same amount of heat passing through them.
In the limit, as you make each little rod smaller and smaller, you end up with an equation that tells you how the temperature at each point in the rod depends on the temperatures on either side of that point - this is a partial differential equation called the heat equation. Solving this equation then tells you how the temperature at each point in the changes over time, and what the steady state temperature is at each point along the rod (if there is a steady state).
@gandalf61 has a good answer. I'll give you another example.
In your scenario, heat is flowing from one end of the rod to the other. Before steady state is reached, the rod is heating up. Therefore, the heat flowing in is greater than the heat flowing out. At steady state, the heat flowing in is equal to the heat flowing out.
At steady state, the rod cannot be at a uniform temperature. This is because heat only flows from high to low temperature. If the rod ends are at the same temperature, then no heat is flowing.
This is analogous to water pressure in a pipe. If the pressure at both ends are equal, then the water in the pipe is being pushed equally from both ends and no flow will occur.
Think about it like this When we heat up a particle (that is provide energy to it) the particle (of solid ) will have some energy absorbed in it. The particle who was earlier vibrating such that it was having lowest possible potential energy, now would not be able to do the same. Due to the energy we added it will vibrate between larger distances it's potential (rather total ) energy will increase. This will cause the whole structure of solid to become a bit less rigid(stable). The solid will obviously try to resist this ( and this is thermal resistance).
Now since the particles resist the change in their energies as we move on from one end( where we heat the rod for example)to other each part recieves less and less heat energy than the previous part.
Due to this the energy which it can absorb decreases and hence temprature starts reducing from one end to other.
Now If you think what if I start adding more heat energy at one end . Still same shall occur one end where heat is applied will have higher temperature and as we move on due to the particles tendency to resist this flow less and less heat shall move ahead. (The energy which the particles resist to flow will get dissipated outside of system through the transfer of the vibrational motion of particles of object to its surrounding ones)
