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Sphere with a core material 1 and a shell material 2, r1, r2, k1, k2 are known, core generates energy with linear function of r

Sphere with a core material 1 and a shell material 2, r1, r2, k1, k2 are known, core generates energy with linear function of r and max energy SC.

Can you please suggest the assumptions and describe the temperature profile across the sphere layers

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