Applied and Computational Mathematics
Volume 5, Issue 6, December 2016, Pages: 234-246
Received: Dec. 19, 2016;
Accepted: Jan. 5, 2017;
Published: Jan. 23, 2017
Views 3268 Downloads 106
Kirthiga Murali, Department of Mathematics, Sethu Institute of Technology, Kariapatti, Tamil Nadu, India
Chitra Devi Mohan, Department of Mathematics, Sethu Institute of Technology, Kariapatti, Tamil Nadu, India
Meena Athimoolam, Department of Mathematics, Saraswathi Narayanan College, Perungudi, Tamil Nadu, India
Rajendran Lakshmanan, Department of Mathematics, Sethu Institute of Technology, Kariapatti, Tamil Nadu, India
The coupled nonlinear system of differential equations in 1-butanol dehydration under atmospheric and isothermal conditions are solved analytically for the microchannel reactor. Approximate analytical expressions of concentrations of 1-butanol, 1-butene, water and dibutyl ether are presented by using homotopy analysis method. The homotopy analysis method eliminated the classical perturbation method problem, because of the existence a small parameter in the equation. The analytical results are compared with the numerical solution and experimental results, satisfactory agreement is noted.
Chitra Devi Mohan,
Mathematical Modelling and Kinetics of Microchannel Reactor, Applied and Computational Mathematics.
Vol. 5, No. 6,
2016, pp. 234-246.
Khan, Y., M, Marin., R, Karinen., J. Lehtonen., J. Kanervo., 2015.1-Butanol dehydration in microchannel reactor: Kinetics and reactor modeling. Chemical Engineering Science, 137: 740–751.
Spatenka, S., V, Fila., B, Bernauer., J, Fulem., G, Germani., Y, Schuurman., 2005. Modeling and simulation of microchannel catalytic WGS reactor for an automotive fuel processor. Chem. Ind. Chem. Eng. Q., 11 (3): 143–151.
Walter, S., S, Malmberg., B, Schmidt., M. A. Liauw., 2005. Mass transfer limitations in micro channel reactors. Catal. Today, 110: 15–25.
Görke, O., P, Pfeifer., K, Schubert., 2009. Kinetic study of ethanol reforming in a microreactor. Appl. Catal. A: Gen., 360: 232–241.
Schmidt, S. A., N, Kumar., A, Reinsdorf., K, Eränen., J, Wärnå., D. Y Murzin., T, Salmi., 2013. Methyl chloride synthesis over Al2O3 catalyst coated micro strucured reactor thermo dynamics. kinetics and mass transfer, Chem. Eng. Sci., 95: 232–245.
Baker, G. A and P, Graves-Morris., in Rota, G. C.(Ed.), 1981. Encyclopaedia of Mathematics, Vol. 13, Pade Approximants, Part II, Addison-Wesley, Reading, MA, Chapter 1.
Rajendran, L., 2000. Padé approximation for ECE and DISP processes at channel electrodes. Electrochemistry Communication, 2: 186-189.
Loghambal, S and L, Rajendran., 2010. Analysis of Amperometric Enzyme electrodes in the homogeneous mediated mechanism using Variational iteration method. Int. J. Electrochem. Sci., 5: 327-343.
Liao, S., 2004. On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation, 147: 499–513.
Meena, A and Rajendran, L., 2010. Analysis of pH-Based Potentiometric Biosensor using Homotopy perturbation method. Chemical Engineering & Technology, 33: 1-10.
Yusufoglu, E., 2009. An improvement to homotopy perturbation method for solving system of linear equations. Computers and Mathematics with Applications, 58: 2231-2235.
Rajendran, L and S, Anitha., 2013. Reply to-Comments on analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method, by Ji-Huan He, Lu-Feng Mo [Electrochim. Acta (2013)]. Electrochimica Acta, 102: 474– 476.
Sen, A. K., 1988. An application of the Adomian decomposition method to the transient behavior of a model biochemical reaction, Journal of Mathematical analysis and applications, 131: 232–245.
El-Sayed, S. M., 2002. The modified decomposition method for solving nonlinear algebraic equations. Applied Mathematics and Computation, 132: 589–597.
Liao, S. J., 1992. The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems, Ph. D. Thesis, Shanghai Jiao Tong University.
Liao, S. J., 1997. An approximate solution technique which does not depend upon small parameters (part 2): an application in fluid mechanics. Int. J. Nonlinear. Mech., 32 (5): 815–822.
Liao, S. J., 2003. Beyond Perturbation: Introduction to the Homotopy Analysis Method. CRC Press, Boca Raton: Chapman & Hall.
Jafari, H., M, Saeidy., J. V. Ahidi., 2009. The homotopy analysis method for solving fuzzy system of linear equations. Int. J. Fuzzy. Syst., 11 (4): 308–313.
Jafari, H., M, Saeidy., M. A. Firoozjaee, 2009. The Homotopy Analysis Method for Solving Higher Dimensional Initial Boundary Value Problems of Variable Coefficients. Numerical Methods for Partial Differential Equations, 26 (5): 1021-1032.
Manimozhi, P and L, Rajendran., 2013. Analytical expression of substrate and enzyme concentration in the Henri-Michaelis-Menten model using Homotopy analysis method. International Journal of Mathematical Archive, 4 (10): 204-214.
Ananthaswamy, V., S. P. Ganesan., L, Rajendran., 2013. Approximate analytical solution of non-linear reaction-diffusion equation in microwave heating model in a slab: Homotopy analysis method. International Journal of Mathematical Archive, 4 (7): 178-189.
Ananthaswamy, V., S, Kala., L, Rajendran., 2014. Approximate analytical solution of non-linear initial value problem for an autocatalysis in a continuous stirred tank reactor: Homotopy analysis method. Int. Journal of Mathematical Archive, 5 (4): 1-12.
Subha M., V, Ananthaswamy., L, Rajendran., 2014. A comment on Liao’s Homotopy analysis method. International Journal of Applied Sciences and Engineering Research, 3 (1): 177-186.
Berteau, P., M, Ruwet., B, Delmon., 1985. Reaction path ways in 1-butanol dehydration on γ-alumina, Bull. Des Sociétés Chim. Belges, 94 (11–12): 859–868.