In heat conduction, what does it actually mean to be in the steady state? I have read about the method of heat conduction and I have some questions related to this topic:
If I consider a metal bar and supply heat in one end, the heat will flow through the bar and if I consider the bar to consist of many layers then each layer absorbs some amount of heat and the rest of the amount will flow to the next layer. So will all the layers attain the steady state at the same time?
And I have read that at steady state all the layers are no longer able to absorb any heat energy. Why can't the layers absorb any heat when they have reached steady state?
 A: Usually in these types of problems (if you want an analytical solution) you keep two ends of the bar at fixed temperatures and it is assumed that other methods of heat loss are not present (convection or radiation form the bar).
The temperature distribution depends on the fixed temperatures at the ends and the conductivity of the material.
The steady state is not attained instantaneously. The heat is transferred slowly and the transfer rate depends on the thermal conductivity.
If you take a section of the bar and the influx from one surface is equal to heat out-flux from other surface (in a time interval dt), which in turn equal to the total heat flow through the bar (in same time interval) the bar is said to be in steady state. In this condition temperature distribution along the bar will not change with time.
If bar is not in steady state the temperature along the bar will change with time and you have to use heat equation to calculate the temperature variation with time.
Usually this can be employed to 1D problems analytically (I am not sure if all the 1D problems can be solved analytically), to solve the real world 2D or 3D situations people usually use Finite element methods to get the transient and steady state solutions.
I hope this will help
regards,
A: When we say a steady state is reached, it means the temperature doesn't change. Along the bar, there is still temperature gradient, which drives the heat flow. 
At steady state, each layer cannot absorb heat. If it can absorb heat, its temperature will increase. This contradicts to the steady state assumption. 
A: Any body can keep absorbing heat if it does not lose heat at all.
But if it constantly loses heat energy, then after some time, the amount of heat it absorbs is compensated by the heat it loses, and hence the difference in temperatures across its conductive surfaces is constant throughout time.
At this point, it achieves a steady state of heat transfer.
