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Numerical Study of a Nonlinear Diffusion Model for Washing of Packed Bed of Cylindrical Fiber Particles

  • Research Article - Chemical Engineering
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Abstract

A nonlinear model representing particle diffusion and molecular diffusion is considered in this paper. The equations are converted into dimensionless form involving Peclet and Biot numbers. The model is discretized in axial and radial domains using a cubic spline collocation method. The system of differential algebraic equations is obtained and is solved using MATLAB ODE15s. Using the actual plant data, the results are examined in terms of relative error. A uniform convergence of order two is established. Also, the model is simulated to study the effect of different parameters on exit solute concentration.

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Abbreviations

B :

Permeability coefficient (m2)

c :

Solute concentration in the fluid (kg/m3)

C F :

Consistency of fibers (kg/m3)

C 0 :

Concentration of solute inside the vat (kg/m3)

D F :

Intrafiber diffusion coefficient (m2/s)

D L :

Longitudinal dispersion coefficient (m2/s)

K :

Dimensionless volumetric equilibrium constant

k f :

Film mass transfer coefficient (m/s)

k 1, k 2 :

Mass transfer coefficients (1/s)

L :

Thickness of packed bed (m)

n :

Solute concentration adsorbed on the fibers (kg/kg)

N 0 :

Initial concentration of solute adsorbed on the fibers (kg/kg)

q :

Concentration of solute inside the pores (kg/m3)

r :

Radial position solute in particle (m)

R :

Fiber radius (m)

Re :

Reynolds number, (= 4ru ρ/μ), dimensionless

t :

Time (s)

u :

Interstitial velocity of liquor through the bed (m/s)

z :

Variable thickness of packed bed (m)

ω :

Porosity of the particle

ɛ :

Porosity of the cake

μ :

Liquid viscosity (Pa s)

ρ :

Liquid density (kg/m3)

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Authors and Affiliations

  1. Department of Mathematics, SLIET, Longowal, 148106, Punjab, India

    Bharti Gupta & V. K. Kukreja

  2. Department of Mathematics, University of KwaZulu-Natal, 4000, Durban, South Africa

    N. Parumasur & P. Singh

Authors
  1. Bharti Gupta
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  2. V. K. Kukreja
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  3. N. Parumasur
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  4. P. Singh
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Correspondence to V. K. Kukreja.

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Gupta, B., Kukreja, V.K., Parumasur, N. et al. Numerical Study of a Nonlinear Diffusion Model for Washing of Packed Bed of Cylindrical Fiber Particles. Arab J Sci Eng 40, 1279–1287 (2015). https://doi.org/10.1007/s13369-015-1633-x

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