(Solution) - Assume steady state one dimensional heat conduction through the symmetric shape shown -(2025 Original AI-Free Solution)

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Assume steady-state, one-dimensional heat conduction through the symmetric shape shown.


Assuming that there is no internal heat generation, derive an expression for the thermal conductivity k(x) for these conditions: A(x) = (1 - x), T(x) = 300(1 - 2x ? x3), and q = 6000 W, where A is in square meters, T in Kelvin?s, and x in meters.