(Solved): From Fourier's Law, show analytically that equation 1 is the correct expression to calculate the hea ...

From Fourier's Law, show analytically that equation 1 is the correct expression to calculate the heat by one-dimensional conduction in a spherical wall of inner radius ???? and outer radius ???? under the following conditions: steady state, constant thermal conductivity, T(r1)=T1,T(r2)=T2

The teacher gave us this to be able to continue with the problem...

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\( Q_{\text {esfera }}=-4 \pi k r_{1} r_{2} \frac{\left(T_{2}-T_{1}\right)}{r_{2}-r_{1}} \) \( A=4 \pi r^{2} \) \( Q=-k \cdot \frac{\partial T}{\partial \eta} \quad \eta=r \) \( Q=-k 4 \pi r^{2} \frac{\partial T}{\partial r} \quad \therefore \quad Q \frac{\partial r}{r^{2}}=-4 \pi k \partial T \)