Consider a spherical pellet with three concentric regions, each with different

thermal conductivities, as shown below. Regions I and II have heat genera$-$

tion rates per unit volume of the functional forms:

Region I $,0r{R}_1,{}_1(r)={}_0[1+(\frac{r}{R_1}{)}^2]$

Region II $,R_{1}r{R}_2,{}_2(r)=\frac{{}_0}{r}$

There is no heat generation in region III and the outer surface is exposed to

a fluid at temperature $T_{}$ and the convective heat transfer coefficient is $($:$h$:$).$