NOMENCLATURE [C.sub.1] constant defined by Equations (8) or (9) ([Pa.sup.-1]) [C.sub.2] constant defined by Equations (8) or (10) ([Pa.sup.-1]) D diffusion coefficient of gas in tube ([m.sup.2]/s) L length of the collector tube (m) M molecular weight (kg/mol) N number of moles (mol) p pressure (Pa) Q gas flow rate (mol/s) r internal radius of tube (m) R universal gas constant
(J/mol K) t time (s) T absolute temperature (K) V volume of the system ([m.sup.3]) x position within the collector tube (m) Greek Symbols [eta] dynamic viscosity of the gas (kg/m s) [[lambda].sub.n] eigenvalue in Equation (17) [tau] dimensionless time defined by Equation (18) (-)
The equation generates one dependent variable t, two dependent variables [alpha] and T, three unknown constants Z, Ea and n, and the universal gas constant
Values assigned to constants used in the numerical model Parameter Value assigned Gas viscosity ([[micro].sub.g], kg/m.s) 1.85 x [10.sup.-5] Water viscosity ([[micro].sub.w] kg/m.s) 1 x [10.sup.-3] Water density ([[rho].sub.w], kg/[m.sup.3]) 1 x [10.sup.3] Universal gas constant
(R, J/K.mol) 8.314 Molecular mass nitrogen ([M.sub.g], kg/mol) 2.8 x [10.sup.-2] Temperature (T, K) 293.15 Acceleration due to gravity (g, m/[s.sup.2]) 9.81 Table 3.
G = pRT/[M.sub.c] 2 where p is density, R the universal gas constant
and T, temperature Kelvin.
where [C.sub.A] and [C.sub.B] are the concentrations (mol/[m.sup.3]) of species in the reactant side, A is the pre- exponential factor ([s.sup.-1]), [E.sub.a] is activation energy (J [mol.sup.-1]) and R is universal gas constant
(J [mol.sup.-1] [K.sup.-1]).
If s (heatingrate) is defined as q dT/dt, and k is expressed as k ko exp(-E/RT), Eq.(2) can be defined asequationwhere, T is the absolute temperature, ko is thefrequency factor, R is the universal gas constant
andE is the activation energy.
In this expression [P.sub.0] is the upstream stagnation pressure; [T.sub.0] is the upstream stagnation temperature; d is the CFV throat diameter; [R.sub.u] is the universal gas constant
; M is molecular weight of dry air; and C* is the real gas critical flow function for dry air--a function of [P.sub.0] and [T.sub.0].
where [k.sub.0] is a constant, [E.sub.r] is the activation energy, and R is the universal gas constant
. The activation energy is usually obtained by experiments and the conversion, [c.sup.*], is determined by
Where: [t.sub.i], seconds, is the cure time at temperature [T.sub.i], [degrees]K; [E.sub.a] is the activation energy, kJ/mole, and R is the universal gas constant
where Z is the compressibility factor, M is the molecular weight, and R is the universal gas constant