The dynamic heat transfer in tube wall

[law&theorem]

When I read some heat transfer book, I got a problem.
There are some numerical calculation methods in dynamic heat conducting in tube wall, but all the methods assume the temperature on one side of the tube and then calculate the temperature distributed in the wall.
But are there some methods assume that temperature on inner/outer sides both changes and then calculate the temperature in the wall ????

[Astronuc]

When I read some heat transfer book, I got a problem.
There are some numerical calculation methods in dynamic heat conducting in tube wall, but all the methods assume the temperature on one side of the tube and then calculate the temperature distributed in the wall.
But are there some methods assume that temperature on inner/outer sides both changes and then calculate the temperature in the wall ???? Sure, it's a matter of transient heat conduction. One has to be familiar with the forms of the steady-state and transient heat conduction equation, or systems of equations for heat transfer.

Normally in calculating temperature through a wall, on starts at the boundary condition and works toward the hottest temperature or axis/plane of symmetry.

Many systems are designed for steady-state, while others may be subject to slow time-varying boundary conditions. In off-normal conditions, the boundary condition may change rapidly with time.

Simulating transients, particularly rapid transients, requires finer time steps (and usually explicit (dynamic) vs implicit (static/quasi-static) numercial solutions). It is also an art.

[law&theorem]

Sure, it's a matter of transient heat conduction. One has to be familiar with the forms of the steady-state and transient heat conduction equation, or systems of equations for heat transfer.

Normally in calculating temperature through a wall, on starts at the boundary condition and works toward the hottest temperature or axis/plane of symmetry.

Many systems are designed for steady-state, while others may be subject to slow time-varying boundary conditions. In off-normal conditions, the boundary condition may change rapidly with time.

Simulating transients, particularly rapid transients, requires finer time steps (and usually explicit (dynamic) vs implicit (static/quasi-static) numercial solutions). It is also an art.

Finer time steps, maybe, I'll try