Temperature rise in a spherical catalyst pellet (Fig. 11B.11) a catalyst pellet has a 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 rate of Sc cal/cm³ ∙ 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. Find the steady-state temperature profile, assuming that Sc is constant throughout. 

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

(b) Set up the differential equation by simplifying the appropriate form of the energy equation. 

(c) Integrate the differential equation to get the temperature profile. Sketch the function T(r). 

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

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

(f) Where in the derivation would one modify the procedure to account for variable k and

Gas temperature T,