The porous catalyst pellet shown in Figure 1 has an overall radius R and a thermal conductivity k (which may be assumed constant). Because of the chemical reaction occurring within the porous pellet, heat is generated at a constant rate of S_{c }cal/cm^{3}.s. Heat is lost at the outer surface of the pellet to a gas stream at a constant temperature by T_{g }convective heat transfer coefficient h.

(a) Make a list of assumptions that apply to the above situation.

(b) Set up the differential equation by making a shell energy balance. Show the

units for all variables that are used.

(c) Specify the proper boundary conditions.

(d) Integrate the differential equation with the above boundary conditions to

obtain an expression for the temperature profile, and make a sketch of the

function profile T(r).

(e) What is the limiting form of T(r) when h→∞?

(f) What is the maximum temperature in the system?

(g) Briefly explain at what point in the derivation of the model equation would

one modify the procedure to account for variable k and S_{c}.

(h) What dimensionless groups could be defined to transform the primitive form

of the solution to one that contains these groups?