Is Heat Transfer between 2 Walls Independent of Temperature Assumptions?

[Shreya]

Homework Statement

Please refer the image
I am not sure if my solution is right, especially about the steady state condition. Am I allowed to assume T' > T1? Or should I consider 2 opposite heat fluxes and figure out their difference
Please be kind to help

Relevant Equations

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The question & my solution

 

[haruspex]

That all looks right.
$T'>T_1$ is a perfectly reasonable assumption, but it does not need to be an assumption if the positive direction for the heat transfer fluxes is defined (rather than taking it be a non-negative quantity). Your equations are valid regardless of the values of the temperatures if the positive flow direction is defined to be from external wall 2 to external wall 1.

 

[Shreya]

That all looks right.
$T'>T_1$ is a perfectly reasonable assumption, but it does not need to be an assumption if the positive direction for the heat transfer fluxes is defined (rather than taking it be a non-negative quantity). Your equations are valid regardless of the values of the temperatures if the positive flow direction is defined to be from external wall 2 to external wall 1.

Thank You! That has really helped @haruspex