The heat flux, $\overrightarrow{\mathbf{q}}^{\prime \prime}$, due to a volume source distribution (expressed in spherical coordinates) is given by:

\[\overrightarrow{\mathbf{q}}_{r}^{\prime \prime}=C r^{2} \sin (\alpha r) \overrightarrow{\mathbf{e}}_{r}\]

a. What is the temperature gradient for this system?

b. If the temperature at $r=0$ is $T=T_{o}$, what is the temperature profile?

c. At what value of $r$ does the solution become physically impossible?