I'm having a technical problem of heat transfer that I can't find the best approach to deal with. I'm grateful for any advice that can point me in the right direction!
Here is an idealised model:
I have a stack of $n$ metal sheets with different temperature on each side of the stack ($T_h$ and $T_c$). Heat is transferred from the hot side to the cold side, we can assume a 1D transfer. The thickness of each plate is $h$ so the total thickness of the stack is $n \times h$, assuming $n$ plates in the stack. $T_h$ and $T_c$ are fixed by circulating fluid.
I know the surface temperatures of both sides of the stack, $T_h$ and $T_c$, and the transfer is in steady state. I also know the thermal conductivity, the density and all properties of the metal. However, thermal conductivity depends on the actual temperature of the metal. I also assume that the sheets are in perfect thermal contact.
Now, I'm removing sheets, one by one, from the cold side of the stack. The surrounding temperatures and hence the surface temperatures $T_h$ and $T_c$, remain the same. We can assume that the surface of the newly exposed sheet will instantly have the temperature of the surrounding medium. The total thickness changes from $n \times h$ to $(n-1) \times h$.
The transfer can no longer be steady state, as the thermal gradient of the top sheets is steeper. Eventually, a new steady state will be reached and the gradient will be readjusted to the new thickness - until I remove another sheet.
I'd think that every removal of a sheet should induce a transient heat pulse.
How can I estimate the heat-flow pulse in response to removal of the sheets (=thinning of the barrier)?
This is not a homework, I could add additional details about the process, but I'm just after the conceptual solution. Any assumptions work.