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Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by residual method

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Abstract

In this paper, two coupled nonlinear differential equations related to carbon dioxide (CO2) and phenyl glycidyl ether (PGE) concentrations are solved using a residual method. This is a particular case of the exp-function method. This model has based a set of boundary conditions for Dirichlet and a mixed set of boundary conditions for Neumann and Dirichlet. This method yields a quick converging, easily computable, and efficiently verifiable approximate closed-form solutions. The numerical result is compared with the approximate solutions obtained by this method and with the other results obtained by the Adomian decomposition method.

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Abbreviations

Symbols:

Description

C A :

Concentration of CO2 (M)

C B :

Concentration of PGE (M)

D A :

Diffusivity of CO2 (m2/s)

D B :

Diffusivity of PGE (m2/s)

K 1 :

Reaction equilibrium constant (1/M)

k 1 :

Forward reaction rate constant in reaction Eq. (2) (1/m2s)

k 2 :

Backward reaction rate constant in reaction Eq. (2) (M/m2s)

k 3 :

Forward reaction rate constant in reaction Eq. (3) (1/m2s)

r A,Cons :

Reaction rate of CO2 in consecutive reaction model (M/s)

St::

Surface area of catalyst (m2)

z :

Distance (m)

\( z_{L} \) :

Film thickness (m)

u :

Normalized concentration of CO2 (None)

v :

Normalized concentration of PGE (None)

\( \alpha_{1} ,\alpha_{2} ,\beta_{1} ,\beta_{2} \,{\text{and}}\,k \) :

Normalized parameters (None)

\( \beta \) :

Flux of CO2 (None)

x :

Dimensionless distance (None)

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Acknowledgment

The Authors are very grateful to the reviewers for their careful and meticulous reading of the paper This work was supported by Academy of Maritime Education and Training (AMET), Deemed to be University, Chennai under seed money project. The Authors are also thankful to Shri J. Ramachandran, Chancellor, Col. Dr. G. Thiruvasagam, Vice-Chancellor, Academy of Maritime Education and Training (AMET), Deemed to be University, Chennai, for their constant encouragement.

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Correspondence to L. Rajendran.

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Appendix

Appendix

Scilab/Matlab program for the numerical solution of the system of nonlinear Eqs. (10) and (11)

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Saranya, K., Mohan, V. & Rajendran, L. Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by residual method. J Math Chem 58, 1230–1246 (2020). https://doi.org/10.1007/s10910-020-01127-0

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