Solution to Design Problem VII

The rate of reaction, Rx, is given by the rate at which species A disappears and is assumed to follow nth-order reaction kinetics given by 

As the two species react the molecular weight of the product increases, leading to an increase in the viscosity of the bulk material. For the polycondensation reaction of species A and B, the weight average molecular weight as a function of the degree of conversion,/ , is (Macosko and Miller, 1976) 

The initial and boundary conditions required to solve Eqs. 8.179,8.180, and 8.181 are similar to those used in Section 8.3 with the exception that the concentration of species A at z = 0 is Cao- The solution of this set of equations requires numerical methods, but a direct finite difference solution is not possible because of the velocity field changing signs near the surface of the screw. To overcome this problem the space-fixed coordinate system is replaced by one that travels along the streamlines. Neglecting the viscous dissipation terms, Eqs. 8.180 and 1.181 become, respectively. 

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