Analytical solution of the advection-diffusion transport equation using a change-of-variable and integral transform technique

International Journal of Heat and Mass Transfer

Volumn 52, Issue 13-14, 2009, Pages 3297-3304

  Perez Guerrero J S ^a   Pimentel, L C G ^b   Skaggs, T H ^c   van Genuchten, M Th ^b  

^a Brazilian Nuclear Energy Commission   (Brazil)

^b FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^c U S SALINITY LABORATORY   (United States)

Author keywords

Analytical solution; Integral transforms; Transport equation

Indexed keywords

ADVECTION - DIFFUSIONS; ADVECTION-DIFFUSION EQUATIONS; ANALYTICAL SOLUTION; CONSTANT COEFFICIENTS; DIFFUSIVE EQUATIONS; EXACT SOLUTIONS; FORMAL SOLUTIONS; INTEGRAL TRANSFORM TECHNIQUES; INTEGRAL TRANSFORMS; NEW SOLUTIONS; NUMERICAL SOLUTIONS; STEADY-STATE REGIMES; TRANSPORT EQUATION;

ADVECTION; COMPUTATIONAL FLUID DYNAMICS; DIFFUSION; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS;

EQUATIONS OF STATE;

EID: 65249163653     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2009.02.002     Document Type: Article

References (25)

1. van Genuchten M.Th. Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-order decay. J. Hydrol. 49 (1981) 213-233
2. Jury W.A., Spencer W.F., and Farmer W.J. Behavior assessment model for trace organics in soil: I. Model description. J. Environ. Qual. 12 (1983) 558-564
3. I. Javandel, C. Doughty, C.F. Tsang, Groundwater Transport: Handbook of Mathematical Models, Water Resources Monograph Series, vol. 10, American Geophysical Union, Washington, DC.
4. Leij F.J., Skaggs T.H., and van Genuchten M.Th. Analytical solutions for solute transport in three-dimensional semi-infinite porous media. Water Resour. Res. 27 10 (1991) 2719-2733
5. Quezada C.R., Clement T.P., and Lee K.K. Generalized solution to multi-dimensional multi-species transport equations coupled with a first-order reaction network involving distinct retardation factors. Adv. Water Resour. 27 5 (2004) 508-521
6. Courant D., and Hilbert D. Methods of Mathematical Physics (1953), Wiley Interscience Publications, New York, USA
7. Morse P.M., and Feshbach H. Methods of Theoretical Physics (1953), McGraw-Hill, New York, USA
8. Carslaw H.S., and Jaeger J.C. Conduction of Heat in Solids. second ed. (1959), Oxford University press, Oxford
9. Sneddon I.N. The Use of Integral Transforms (1972), McGraw-Hill
10. Ozisik M.N. Heat Conduction (1980), Wiley, New York
11. Leij F.J., and van Genuchten M.Th. Analytical modeling of nonaqueous phase liquid dissolution with Green's functions. Transport in Porous Media 38 (2000) 141-166
12. Mikhailov M.D., and Ozisik M.N. Unified Analysis and Solutions of Heat and Mass Diffusion (1984), John Wiley & Sons
13. Cotta R.M. Integral Transforms in Computational Heat and Fluid Flow (1993), CRC Press, Boca Raton, FL
14. Zwillinger D. Handbook of Differential Equations (1992), Academic Press
15. Polyanin A.D. Handbook of Linear Partial Differential Equations for Engineers and Scientists (2002), Chapman & Hall/CRC Press, Boca Raton
16. R.B. Codell, K.T. Key, G.A Whelan, Collection of Mathematical Models for Dispersion in Surface Water and Groundwater, NUREG 0868, U.S. Nuclear Regulatory Commission, Washington, DC, 1982.
17. M. Th. van Genuchten, W.J. Alves, Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation, USDA ARS Technical Bulletin Number 1661, U.S. Salinity Laboratory, 1982.
18. Wexler E.J. Analytical Solutions for One-, Two-, and Three-Dimensional Solute Transport in Ground-Water Systems with Uniform Flow (1992), U.S. Geological Survey Techniques of Water-Resources Investigations Book 3, Chapter B7
19. Brenner H. The diffusion model of longitudinal mixing in beds of finite length. Numerical values. Chem. Eng. Sci. 17 (1962) 229-243
20. Selim H.M., and Mansell R.S. Analytical solution of the equation of reactive solutes through soils. Water Resour. Res. 12 (1976) 528-12532
21. W.J. Golz, Solute Transport in a Porous Medium: A Mass-Conserving Solution for the Convection-Dispersion Equation in a Finite Domain. Ph.D. thesis, Louisiana State University, 2003.
22. IMSL Library, MATH/LIB, Houston, TX, 1987.
23. van Genuchten M.Th. Convective-dispersive transport of solutes involved in sequential first-order decay reactions. Comput. Geosci. 11 2 (1985) 129-147
24. MATHEMATICA, Wolfram Research, Inc., Champaign, IL, 2004.
25. J. Simunek, M. Th. van Genuchten, M. Sejna, N. Toride, F.J. Leij, The STANMOD computer software for evaluating solute transport in porous media using analytical solutions of convection-dispersion equation, Versions 1.0 and 2.0, IGWMC-TPS-71, International Ground Water Modeling Center, Colorado School of Mines, Golden, Colorado, 1999.