Fourier's Equations: difficult problem

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The discussion revolves around solving a heat transfer problem involving a series of insulators with varying thermal conductivity (kappa) due to significant temperature differences. The user is attempting to calculate the heat transfer rate (Q/t) for a system consisting of a cylinder in series and disks in parallel, while accounting for the linear variation of kappa with temperature. They have started by separating and integrating the relevant equations but are struggling to establish a general form for their calculations. The user is uncertain whether the problem is transient or steady state and suggests that a visual representation might aid in understanding. Clarifying these aspects is crucial for accurately solving the problem.
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Homework Statement


So I have a problem where I have a series and two other parallel insulators bringing a system from a temperature of Tzero to Ttwo. However, the two aforementioned temperatures have a huge difference thus causing kappa to vary with temperature. I am trying to know how to solve for Q/t of the whole system accounting for the varying kappa with temperature (assume the kappa function is linear with temperature change (y=mx+b form)). So I have a cylinder that is in series (2*pi*r*L) and top and bottom that are parallel but not series (disks with thickness).

Homework Equations


Q/t=kAdT/dx

The Attempt at a Solution


I serperated and integrated. I set Q/t=Q/t for the series from where they change. The difficulty I have is coming up with the general form (T-t)/R and using that to do stuff.
 
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Is this a transient problem or a steady state problem?
 
I think we need a picture ...
 

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