Effectiveness factor nonisothermal model

Do an order-of-magnitude calculation for the nonisothermal effectiveness factor. Hint Use the pore model to estimate an isothermal effectiveness factor and obtain from that. Assume k ff = 0.15 J m s K. 

In the previous examples, we have exploited the idea of an effectiveness factor to reduce fixed-bed reactor models to the same form as plug-flow reactor models. This approach is useful and solves several important cases, but this approach is also limited and can take us only So far. In the general case, we must contend with multiple reactions that are not first order, nonconstant thermochemical properties, and nonisothermal behavior in the pellet and the fluid. For these cases, we have no alternative but to solve numerically for the temperature and species concentrations profiles in both the pellet and the bed. As a final example, we compute the numerical solution to a problem of this type. 

Since the major thermal resistances in nonisothermal reaction systems are encountered in the boundary layer, while the major mass transfer resistances occur within the particle, we can entertain some simplification of the overall effectiveness factor problem we have been considering. This simplified model envisions interphase temperature gradients and intraphase concentration gradients only. For this case... 

The classic extrusion model gives insight into the screw extrusion mechanism and first-order estimates. For more accurate design equations, it is necessary to eliminate a long series of simplifying assumptions. These, in the order of significance are (a) the shear rate-dependent non-Newtonian viscosity (b) nonisothermal effects from both conduction and viscous dissipation and (c) geometrical factors such as curvature effects. Each of these... 

Use of the CSTR sequence as a model for nonideal reactors has been criticized on the basis that it lacks certain aspects of physical reality, such as the absence of backward communication between the individual mixing cell units. Such may be the case nonetheless the mathematical simplicity of the approach makes it very attractive, particularly for systems with complex kinetics, nonisothermal effects, or other complicating factors. 

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