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Mathematical modeling of turbulent heat and mass transfer with chemical conversions

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Abstract

A transient model of heat and mass transfer with nonlinear sources (sinks) caused by first-and second-order chemical reactions is developed. The model uses a matching condition (equal temperature and local flux values) at the reaction zone-coolant interface. A finite-difference numerical solution to the problem is obtained using the alternating direction method. The model is tested by application to fast polymerization processes. The effect of the coolant velocity, reactor radius, and coolant temperature at the reactor inlet on the polymerization efficiency is studied.

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Abbreviations

c:

concentration, mol/m3

c p :

specific heat capacity, J/(kg K)

\(\tilde D\) :

diffusion tensor

D T :

averaged coefficient of turbulent diffusion, m2/s

E a :

effective activation energy for the reaction of monomer with active site (chain growth), J

E b :

effective activation energy for the chain termination reaction, J

F:

vector of body forces

f 1, f 2, f 3 :

parameters of hyperbolic equation, s

h i :

longitudinal (axial) discretization step

h j :

radial discretization step

h τ :

discretization step in time

K a :

specific rate for the reaction of monomer with active site (chain growth), m3/(mol s)

K b :

specific rate for the chain termination reaction, 1/s

k:

parameter accounting for the separate supply of monomer and catalyst

k a :

preexponential factor for the rate of reaction between monomer and active site (chain growth), m3/(mol s)

k b :

preexponential factor for the chain termination reaction, 1/s

L:

reactor length, m

P:

tensor of surface forces

Q a :

molar heat for the reaction between monomer and active site, J/mol

R:

universal gas constant, J/(mol K)

R 2 :

tubular reactor radius, m

R 3 :

cooling zone “radius,” m

r 2 :

radial coordinate in zone II, m

r 3 :

radial coordinate in zone III, m

r 20 :

conversion factor for writing r 2 in dimensionless form, m

r 30 :

conversion factor for writing r 3 in dimensionless form, m

\(\bar r_2 \) :

dimensionless radial coordinate in zone II

\(\bar r_3 \) :

dimensionless radial coordinate in zone III

T:

temperature, K

T * :

characteristic temperature in the modified Arrhenius equation, K

t:

dimensionless time

u:

velocity vector

u:

averaged value of velocity, m/s

x:

longitudinal coordinate, m

\(\bar x\) :

dimensionless longitudinal coordinate

β = RT */E a :

dimensionless parameter

ηa :

characteristic time for the reaction between monomer and active site, s

ηb :

characteristic time for the chain termination reaction, s

ϑ:

dimensionless temperature

\(\tilde \lambda \) :

thermal conductivity tensor

λ:

thermal conductivity, J/(m s K)

λ*:

effective thermal diffusivity, m2/s

λT :

averaged thermal conductivity, J/(m s K)

ρ:

density, kg/m3

τ:

time, s.

a:

monomer

b:

catalyst (active site)

0:

initial value

1:

value at reactor inlet

2:

zone II

3:

zone III

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Authors and Affiliations

  1. Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka Moscow oblast, 142432, Russia

    L. P. Kholpanov

  2. USPolyResearch, Ashland, PA, 17921, USA

    Yu. S. Polyakov

Authors
  1. L. P. Kholpanov
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  2. Yu. S. Polyakov
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Original Russian Text © L.P. Kholpanov, Yu.S. Polyakov, 2006, published in Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 2006, Vol. 40, No. 5, pp. 490–500.

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Kholpanov, L.P., Polyakov, Y.S. Mathematical modeling of turbulent heat and mass transfer with chemical conversions. Theor Found Chem Eng 40, 454–464 (2006). https://doi.org/10.1134/S0040579506050022

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