a A spherical catalyst pellet with radius R and thermal conductivity k was added into a bottle of chemical for boosting reaction. The catalytic reaction releases heat at a uniform heat rate per unit volume S (J/s-m) throughout the catalyst. Assume the whole system remains steady-state, thermal conductivity k is constant and the radius of catalyst is unchanged. The heat transfer coefficient of the chemical is h, the temperature of chemical remains Tc. (a) Derive the governing equation of the catalyst by shell balance (b) Write down the boundary conditions for solving the equation (c) Calculate the temperature profile of this catalyst (d) Calculate the heat outflow rate of surface Chemical Catalyst