**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31023

##### Analysis of One Dimensional Advection Diffusion Model Using Finite Difference Method

**Authors:**
Vijay Kumar Kukreja,
Ravneet Kaur

**Abstract:**

**Keywords:**
Stability,
Consistency,
Crank-Nicolson scheme,
Lax-Richtmyer theorem,
Peclet number,
Gerschgorin
circle

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.3566325

**References:**

[1] H. Kopka and P. W. Daly, A Guide to LATEX, 3rd ed. Harlow, England: Addison-Wesley, 1999.

[2] H. Brenner, The diffusion model of longitudinal mixing in beds of finite length. Numerical values, Chem. Eng. Sci. 17(4) (1962) 229-243.

[3] J. Crank, P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type, Proc. Cambridge Philosophy Soc. 43(1) (1947) 50-67.

[4] M.J. Cocero, J. Garcia, Mathematical model of supercritical extraction applied to oil seed extraction by CO2+ saturated alcohol I.Desorption model, J. Supercritical Fluids 20(3) (2001) 229-243.

[5] P.V. Danckwerts, Continuous flow systems distribution of residence times, Chem. Eng. Sci. 2(1) (1953) 1-44.

[6] S. Farooq, I.A. Karimi, Dispersed plug flow model for steady-state laminar flow in a tube with a first order sink at the wall, Chem. Eng. Sci. 58(1) (2003) 7180.

[7] M. Feiz, A 1-D multigroup diffusion equation nodal model using the orthogonal collocation method, Annals of Nuclear Energy 24(3) (1997) 187-196.

[8] L. Gardini, A. Servida, M. Morbidelli, S. Carra, Use of orthogonal collocation on finite elements with moving boundaries for fixed bed catalytic reactor simulation, Comp. Chem. Eng. 9(1) (1985) 1-17.

[9] B. Giojelli, C. Verdier, J.Y. Hihn, J.F. Beteau, A. Rozzi, Identification of axial dispersion coefficients by model method in gas/liquid/solid fluidised beds, Chem. Eng. P. 40(2) (2001) 159-166.

[10] C. Grossman, H.G. Roos, M. Stynes, Numerical Treatment of Partial Differential Equations, Springer-Verlag, Heidelberg 2007.

[11] S. Karacan, Y. Cabbar, M. Alpbaz, H. Hapoglu, The steady-state and dynamic analysis of packed distillation column based on partial differential approach, Chem Eng. P. 37(5) (1998) 379-388.

[12] I.A. Khan, K.F. Loughlin, Kinetics of sorption in deactivated zeolite crystal adsorbents, Comp. Chem. Eng. 27(5) (2003) 689-696.

[13] J.H. Koh, P.C. Wankat, N.H.L. Wang, Pore and surface diffusion and bulk-phase mass transfer in packed and fluidized beds, Ind. Eng. Chem. Res. 37(1) (1998) 228-239.

[14] V.K. Kukreja, A.K. Ray, V.P. Singh, N.J. Rao, A mathematical model for pulp washing on different zones of a rotary vacuum filter, Indian Chem. Eng., Sec- A 37(3) (1995) 113-124.

[15] V.K. Kukreja, A.K. Ray, Mathematical modeling of a rotary vacuum washer used for pulp washing: A case study of a lab scale washer, Cell. Chem. Tech. 43(1-3) (2009) 25-36.

[16] L. Lefevre, D. Dochain, S.F. Azevedo, A. Magnus, Optimal selection of orthogonal polynomials applied to the integration of chemical reactor equations by collocation methods, Comp. Chem. Eng. 24(12) (2000) 2571-2588.

[17] J.R. LeVeque, R. Bali, Finite Difference Methods for Ordinary and Partial Differential Equations Steady-State and Time-Dependent Problems, SIAM, Philadelphia, 2007.

[18] W.S. Long, S. Bhatia, A. Kamaruddin, Modeling and simulation of enzymatic membrane reactor forkinetic resolution of ibuprofen ester, J. Membrane Sci. 219(1-2) (2003) 69-88.

[19] C.G. Mingham, D.M. Causon, Introductory Finite Difference Methods for PDEs, Ventus Publishing, 2010.

[20] F. Potucek, Washing of pulp fibre beds, Collect. Czech. Chem. Commun. 62(4) (1997) 626-644.

[21] A.K. Ray, V.K. Kukreja, Solving pulp washing problems through mathematical models, AIChE Symposium Series, 96(324) (2000) 42-47.

[22] R.D. Richtmyer, K.W. Morton, Difference Methods for Initial Value Problems, Interscience Publishers, John Wiley & Sons, New York, 1967.

[23] L. Sajc, G.V. Novakovic, Extractive bioconversion in a four-phase external-loop airlift bioreactor, AIChE J. 46(7) (2000) 1368-1375.

[24] N.V. Saritha, G. Madras, Modeling the chromatographic response of inverse size-exclusion chromatography, Chem. Eng. Sci. 56(23) (2001) 6511-6524.

[25] G.D. Smith, Numerical Solutions of Partial Differential Equations: Finite Difference Methods, Clarendon press-Oxford, New York, 1985.

[26] P. Sridhar, Implementation of the one point orthogonal collocation method to an affinity packed bed model, Ind. Chem. Eng., Sec. A 41(1) (1999) 39-46.

[27] J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM, Philadelphia 2004.

[28] L.M. Sun, F. Meunier, An improved finite difference method for fixed bed multicomponent sorption, AIChE J. 37(2) (1991) 244-254.

[29] M.K. Szukiewicz, New approximate model for diffusion and reaction in a porous catalyst, AIChE J. 46(3) (2000) 661-665.