Problem $6$

A spherical wall contains a hot fluid, which creates an

elevated temperature at its inner wall $(T_{s1}$ located at $r=r_1).$

The outer wall loses heat to the ambient, causing its surface

temperature $(T_{s2}$ located at $r=r_2)$ to be cooler than that of

the inner wall. Assuming temperature variation only in the $r-$

direction and with the constant surface temperatures shown

as boundary conditions, solve for the steady$-$state

temperature profile, $T(r).$