Centerline reactant fraction

The deposition modulus at low temperatures is small, and the profile of the reactant concentration through the preform thickness is very uniform. In this case, the deposition rate at the center is nearly as large as that at the preform surface. With increasing temperature, the deposition modulus increases and the reactant concentration at the preform center falls. In this case, the centerline deposition rate becomes small relative to that at the surface. This behavior is illustrated in Figure 2. Here we see that the normalized centerline reactant fraction falls monotonically with increasing values of the deposition modulus. The centerline reactant fraction does not exhibit any sort of maximum, as is well known, and the deposition uniformity, U = /, falls smoothly as the deposition modulus is increased. 

Under the further restriction that corresponding to 7 0, the last term on the left of Eq. 36 may be neglected. This special case yields P 4.2656 and a corresponding centerline reactant fraction of 0.2495. The optimum temperature can then be obtained by using the optimum pressure,/ = 2, in Eq. 23. This gives... 

Optimum temperatures are obtained from the analytical expressions describing the optimum conditions, along with the derivative of the centerline reactant fraction with respect to the deposition modulus. Using an analytical solution to provide the derivative of the centerline reactant fraction, a closed-form implicit expression for the optimum temperature is obtained for the special case of no normalized reaction yield. For the more general case, this derivative is computed from numerical solutions to the equations governing transport and deposition. Optimum temperatures are presented graphically for a very wide range of the normalized preform thickness and normalized reaction yield. 

A second useful normalization of the deposition rate is the simple modification of S given by S = Note that the normalized centerline deposition rate can be obtained from Eqs.22a, b simply by taking/ =f where/ is the normalized reactant fraction at z = 0. The pressure, temperature and all other variables in these expressions are uniform over the preform thickness. 

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