A spherical shell of inner radius, $r_{i}$, outer radius, $r_{o}$, and thermal conductivity, $k$, is being used to dissipate heat. At a particular time, the temperature profile within the shell is measured and found to be:

\[T(r)=\frac{C_{1}}{r}+C_{2}\]

a. Is the heat transfer at steady state, i.e., is the rate constant?

b. How does the heat flow rate vary with position?