Reconsider diffusion and reaction in a spherical catalyst pellet for the case where the reaction is not isothermal. Show that the energy balance can be written as
where kt is the effective thermal conductivity, cal/s cm • K of the pellet with dT/dr = 0 at r = 0 and T = Ts at r = R.
(a) Evaluate Equation (12–11) for a first-order reaction and combine with Equation (P12-13.1) to arrive at an equation giving the maximum temperature in the pellet.
Note: At Tmax, CA = 0.
(b) Choose representative values of the parameters and use a software package to solve Equations (12–11) and (P12-13.1) simultaneously for T(r)andCA(r) when the reaction is carried out adiabatically. Show that the resulting solution agrees qualitatively with Figure 8.
Figure 8 Swimming of an organism.
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