- About this Journal ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
ISRN Physical Chemistry
Volume 2013 (2013), Article ID 487240, 14 pages
Analytical Solution of Non-Isothermal Diffusion-Reaction Processes and Effectiveness Factors
Department of Mathematics, The Madura College, TamilNadu, Madurai 625011, India
Received 13 September 2012; Accepted 31 October 2012
Academic Editors: J. M. Farrar, E. B. Starikov, and A. Vergara
Copyright © 2013 Vembu Ananthaswamy and Lakshmanan Rajendran. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. T. Villa, N. A. Acosta, and C. M. Albarracin, “A note on non-isothermal diffusion-reaction processes,” International Journal of Pure and Applied Mathematics, vol. 71, no. 4, pp. 525–538, 2011.
- D. Bedeaux, I. Pagonabarraga, J. M. Ortiz De Zárate, J. V. Sengers, and S. Kjelstrup, “Mesoscopic non-equilibrium thermodynamics of non-isothermal reaction-diffusion,” Physical Chemistry Chemical Physics, vol. 12, no. 39, pp. 12780–12793, 2010.
- G. F. Froment and K. B. Bischoff, Chemical Reactor Analysis and Design, John Wiley & Sons, New York, NY, USA, 2nd edition, 1990.
- S. Kjelstrup, J. M. Rubi, and D. Bedeaux, “Energy dissipation in slipping biological pumps,” Physical Chemistry Chemical Physics, vol. 7, no. 23, pp. 4009–4018, 2005.
- A. S. Blix, Arctic Animals, Tapir Academic, Trondheim, Norway, 2001.
- D. Bedeaux and S. Kjelstrup, “The measurable heat flux that accompanies active transport by Ca2+-ATPase,” Physical Chemistry Chemical Physics, vol. 10, no. 48, pp. 7304–7317, 2008.
- E. Johannessen and S. Kjelstrup, “Numerical evidence for a “highway in state space” for reactors with minimum entropy production,” Chemical Engineering Science, vol. 60, no. 5, pp. 1491–1495, 2005.
- S. Kjelstrup, D. Bedeaux, and E. Johannessen, Elements of Irreversible Thermodynamics for Engineers, Tapir Academic, Trondheim, Norway, 2007.
- L. V. Van Der Ham, J. Gross, A. Verkooijen, and S. Kjelstrup, “Efficient conversion of thermal energy into hydrogen: comparing two methods to reduce exergy losses in a sulfuric acid decomposition reactor,” Industrial and Engineering Chemistry Research, vol. 48, no. 18, pp. 8500–8507, 2009.
- C. M. Guldberg and P. Waage, ForhandlInger: VIdenskabs-Selskabet i ChrIstIanIa, 1864.
- H. Eyring and E. Eyring, Modern Chemical Kinetics, Chapman & Hall, London, UK, 1965.
- L. Onsager, “Reciprocal relations in irreversible processes. I,” Physical Review, vol. 37, no. 4, pp. 405–426, 1931.
- L. Onsager, “Reciprocal relations in irreversible processes. II,” Physical Review, vol. 38, no. 12, pp. 2265–2279, 1931.
- H. A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica, vol. 7, no. 4, pp. 284–304, 1940.
- I. Prigogine and P. Mazur, “Sur l'extension de la thermodynamique aux phénomènes irreversibles liés aux degrés de liberté internes,” Physica, vol. 19, no. 1–12, pp. 241–254, 1953.
- S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, North-Holland, Amsterdam, The Netherlands, 1962.
- D. Reguera, J. M. Rubí, and J. M. G. Vilar, “The mesoscopic dynamics of thermodynamic systems,” Journal of Physical Chemistry B, vol. 109, no. 46, pp. 21502–21515, 2005.
- I. Pagonabarraga, A. Pérez-Madrid, and J. M. Rubí, “Fluctuating hydrodynamics approach to chemical reactions,” Physica A, vol. 237, no. 1-2, pp. 205–219, 1997.
- I. Pagonabarraga and J. M. Rubí, “Derivation of the Langmuir adsorption equation from non-equilibrium thermodynamics,” Physica A, vol. 188, no. 4, pp. 553–567, 1992.
- D. Reguera and J. M. Rubí, “Nonequilibrium translational-rotational effects in nucleation,” Journal of Chemical Physics, vol. 115, no. 15, pp. 7100–7106, 2001.
- J. M. Rubi and S. Kjelstrup, “Mesoscopic nonequilibrium thermodynamics gives the same thermodynamic basis to Butler-Volmer and Nerst equations,” Journal of Physical Chemistry B, vol. 107, no. 48, pp. 13471–13477, 2003.
- Y. Demirel and S. I. Sandler, “Effects of concentration and temperature on the coupled heat and mass transport in liquid mixtures,” International Journal of Heat and Mass Transfer, vol. 45, no. 1, pp. 75–86, 2001.
- S. Kjelstrup and D. Bedeaux, “Elements of irreversible thermodynamics for engineers,” in Applied Thermodynamics, A. H. Goodwin, J. V. Sengers, and C. J. Peters, Eds., IUPAC Chemical Data Series no. XX, chapter 14, Royal Society of Chemistry, London, UK, 2010.
- Y. Demirel, “Non-isothermal reaction-diffusion systems with thermodynamically coupled heat and mass transfer,” Chemical Engineering Science, vol. 61, no. 10, pp. 3379–3385, 2006.
- Y. Demirel, “Modeling of thermodynamically coupled reaction-transport systems,” Chemical Engineering Journal, vol. 139, no. 1, pp. 106–117, 2008.
- J. M. Ortiz de Zárate and J. V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures, Elsevier, Amsterdam, The Netherlands, 2006.
- B. Hafskjold and S. K. Ratkje, “Criteria for local equilibrium in a system with transport of heat and mass,” Journal of Statistical Physics, vol. 78, no. 1-2, pp. 463–494, 1995.
- J. Xu, S. Kjelstrup, D. Bedeaux, and J. M. Simon, “Transport properties of 2F ⇄ F2 in a temperature gradient as studied by molecular dynamics simulations,” Physical Chemistry Chemical Physics, vol. 9, no. 8, pp. 969–981, 2007.
- J. Xu, S. Kjelstrup, and D. Bedeaux, “Molecular dynamics simulations of a chemical reaction; Conditions for local equilibrium in a temperature gradient,” Physical Chemistry Chemical Physics, vol. 8, no. 17, pp. 2017–2027, 2006.
- A. Vergara, F. Capuano, L. Paduano, and R. Sartorio, “Lysozyme mutual diffusion in solutions crowded by poly(ethylene glycol),” Macromolecules, vol. 39, no. 13, pp. 4500–4506, 2006.
- T. Ikeda, M. Boero, and K. Terakura, “Hydration of alkali ions from first principles molecular dynamics revisited,” Journal of Chemical Physics, vol. 126, no. 3, Article ID 034501, 9 pages, 2007.
- J. H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, pp. 257–262, 1999.
- J. H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73–79, 2003.
- J. H. He, “A simple perturbation approach to Blasius equation,” Applied Mathematics and Computation, vol. 140, no. 2-3, pp. 217–222, 2003.
- P. D. Ariel, “Alternative approaches to construction of Homotopy perturbation Algorithms,” Nonlinear Science Letters, vol. 1, pp. 43–52, 2010.
- Q. K. Ghori, M. Ahmed, and A. M. Siddiqui, “Application of homotopy perturbation method to squeezing flow of a newtonian fluid,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 179–184, 2007.
- T. Öziş and A. Yildirim, “A comparative study of He's Homotopy Perturbation Method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 243–248, 2007.
- S. J. Li and Y. X. Liu, “An improved approach to nonlinear dynamical system identification using PID neural networks,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 2, pp. 177–182, 2006.
- M. M. Mousa and S. F. Ragab, “Application of the homotopy perturbation method to linear and nonlinear schrödinger equations,” Zeitschrift für Naturforschung, vol. 63, no. 3-4, pp. 140–144, 2008.
- V. Ananthaswamy and L. Rajendran, “Analytical Solution of Non-Linear Kinetic equation in a porous pellet,” Global Journal of Pure and Applied Mathematics, vol. 8, pp. 101–111, 2012.
- S. Loghambal and L. Rajendran, “Mathematical modeling of diffusion and kinetics in amperometric immobilized enzyme electrodes,” Electrochimica Acta, vol. 55, no. 18, pp. 5230–5238, 2010.
- A. Meena and L. Rajendran, “Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations—homotopy perturbation approach,” Journal of Electroanalytical Chemistry, vol. 644, no. 1, pp. 50–59, 2010.
- A. Shanmugarajan, S. Alwarappan, S. Somasundaram, and R. Lakshmanan, “Analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method,” Electrochimica Acta, vol. 56, no. 9, pp. 3345–3352, 2011.
- V. Ananthaswamy and L. Rajendran, “Analytical solution of two-point non linear boundary value problems in a porous catalyst particles,” International Journal of Mathematical Archieve, vol. 3, no. 3, pp. 810–821, 2012.