Temperature rise in a spherical catalyst pellet. A catalyst pellet has a radius $R$ and a

thermal conductivity $k($constant$).$ Because of a chemical reaction occurring in the porous

pellet, heat is generated at a rate of $Sc$ in $ca\frac{l}{c}{m}^3*s.$ Heat is lost at the outer surface of the

pellet to a gas stream at constant temperature $T_g$ by convective heat transfer with heat

transfer coefficient $h.$

a$)$ Perform a dimensional analysis of the governing differential equation before solving

by using a dimensionless temperature defined as $T^{**}=\frac{T-T_g}{T_g}$ and determine an

expression for a dimensionless volumetric heating rate, $S{c}^{**}.$ Demonstrate that

dimensional analysis of the boundary condition yields the Biot number: $Bi-=h\frac{R}{k}.$

Finally, find the steady$-$state dimensionless temperature profile, $T^{**}(r^{**}).$

b$)$ Using your choice of computational approach $($preferably MATLAB, but Excel can

work$)$ plot the temperature profiles for $S_c^{**}=3$ and $Bi=0\mathrm{.}1,1\mathrm{.}0$ and $10$ on one plot.

Discuss and interpret how the temperature distribution changes for the different $Bi$

numbers. Include your M file code or your Excel file.