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Nonisothermal non-Newtonian chemical reactions in a tubular reactor under conditions of variable viscosity

Abstract

The nonisothermal non-Newtonian chemical reactions in a tubular reactor are investigated. The non-Newtonian fluid is assumed to be characterized by the Ostwald-de Waele power-law model, which represents the majority of laminar flow of food products and many polymer melts and solutions. The temperature effect on the viscosity is considered and is found to be very significant. The effects of other important dimensionless parameters on the reactor performances are examined.

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Abbreviations

c :

mass fraction of reactant

c 0 :

inlect mass fraction of reactant

C p :

heat capacity, J/kg K

C :

dimensionless concentration of reactant, c/c 0

C b :

dimensionless bulk concentration of reactant

D :

molecular diffusivity, m2/s

ΔE :

activation energy, J/kg

ΔH :

heat of reaction, J/m3

k 1 :

frequency factor, s−1

k t :

heat conductivity, J/m K kg

K :

fluid consistency, kg sn−1/m

K 1 :

dimensionless frequency factor, k 1 r 0 2 c m−1 exp(−β1)/D

K 0 :

constant in Eq. (6)

m :

order of chemical reaction

n :

rheological parameter

p :

pressure, kg/m s2

r :

radial coordinate, m

r 0 :

radius of reactor, m

R :

dimensionless radial coordinate, r/r 0

R g :

gas constant, J/kg K

T :

temperature, K

T 0 :

inlet temperature, K

u :

velocity, m/s

u b :

bulk velocity, m/s

U :

dimensionless velocity, u/u b

x :

axial coordinate, m

X :

dimensionless axial coordinate, xD/r 0 2 u b

α :

dimensionless parameter, \(k_t /{}_\rho C_{\text{p}} D\)

β :

dimensionless parameter, β 0T0

β 1 :

dimensionless activation energy, ΔE/R g T 0

β 2 :

dimensionless heat generation, \(( - \Delta {\rm H}{\text{)/}}{}_\rho C_{\text{p}} T_0 \)

θ :

dimensionless temperature, (T−T 0)/T 0

θ b :

dimensionless bulk temperature

ρ :

liquid density, kg/m3

References

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Lin, S.H. Nonisothermal non-Newtonian chemical reactions in a tubular reactor under conditions of variable viscosity. Appl. Sci. Res. 32, 195–206 (1976). https://doi.org/10.1007/BF00383715

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Keywords

  • Polymer
  • Viscosity
  • Food Product
  • Temperature Effect
  • Laminar Flow