Reaction in a Slab

For a second order reaction in a slab or a sphere, analytical solutions proceed in terms of elliptic functions beyond the solution of P7.03.ll, although a numerical solution throughout may be preferable. Such a numerical procedure is adopted in P7.03.19 for a second order reversible reaction. 

For a first order reaction in a slab the rate of reaction thus becomes,... 

P7.03.10. SECOND ORDER REACTION IN A SLAB. NUMERICAL INTEGRATION The differential equation is derived in problem P7.03.01,... 

ZLQhJX. SECOND ORDER REACTION IN A SLAB. ANALYTICAL SOLUTION... 

While we have contact with this problem, however, we will look at the asymptotics of reactions in a slab of catalyst. In Chapter 3 we used the special form of the equations for diffusion and reaction to get rather general expressions for the Thiele modulus and effectiveness in terms of the center concentration v... 

Figure 7-lQs shows the ratio of the effectiveness factor with uniform poisoning to that without poisoning versus the fraction poisoned for the above case of first-order reaction in a slab. 

Figure 7.3 Effectiveness factors for a first-order reaction in a slab (P), cylinder (Q, and sphere (S) as functions of the Thiele moduli for the three shapes (Aris, 1969).

To illustrate the salient features of the method, we first consider the following boundary value problem in an abstract form, and then later attempt an elementary example of diffusion and reaction in a slab of catalyst material. We shall assume there exists an operator of the type discussed in Chapter 2 (Section 2.5) so that in compact form, we can write... 

We illustrate the above five variations of weighted residuals with the following example of diffusion and first order chemical reaction in a slab catalyst (Fig. 8.1). We choose the first order reaction here to illustrate the five methods of weighted residual. In principle, these techniques can apply equally well to nonlinear problems, however, with the exception of the collocation method, the integration of the form (8.7) may need to be done numerically. 

We illuminate these attractive features by considering the difficult problems of diffusion and reaction in a slab catalyst sustaining highly nonlinear Hinshelwood kinetics. The mass balance equations written in nondimensional form are taken to be... 

Tavera EM. Analytical expression for the non-isothermal effectiveness factor The nth-order reaction in a slab geometry. Chemical Engineering Science 2005 60 907-916. 

Internal Pore Diffusion and Reaction in a Slab-Shaped Catalyst Pellet... 

The multiplicity of solutions at finite time values may be analyzed more explicitly by applying the following treatment of Amundson and Raymond [17] to noncatalytic gas-solid reactions in a slab. Equation (4.3.100) may be written for an infinite slab as follows ... 

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