Critical times in single-layer reaction diffusion

International Journal of Heat and Mass Transfer

Volumn 54, Issue 11-12, 2011, Pages 2642-2650

  Hickson, R I ^a,b   Barry, S I ^a,b   Sidhu, H S ^a   Mercer, G N ^a,b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b The Australian National University   (Australia)

Author keywords

Critical time; Diffusion; Reaction diffusion; Time scale

Indexed keywords

CRITICAL TIME; DIFFUSION PROCESS; DIFFUSION TIME; EXACT SOLUTION; LINEAR REACTION; REACTION DIFFUSION; SINGLE LAYER; TIME SCALE;

MEDICAL PROBLEMS; TIME MEASUREMENT;

DIFFUSION;

EID: 79953057947     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2011.01.019     Document Type: Article

References (40)

1. Y. Demirel Thermodynamically coupled heat and mass flows in a reaction-transport system with external resistances Int. J. Heat Mass Transfer 52 2009 2018 2025
2. T. Gambaryan-Roisman, E. Litovsky, M. Shapiro, and A. Shavit Reaction-diffusion model of surface and grain boundary segregation kinetics Int. J. Heat Mass Transfer 43 2000 4135 4151
3. C. Li False diffusion in convection and diffusion with chemical reaction Int. J. Heat Mass Transfer 26 7 1983 1063 1067 (Pubitemid 13590067)
4. G. Fulford, and P. Broadbridge Industrial Mathematics: Case Studies in the Diffusion of Heat and Matter 2002 Cambridge University Press Cambridge, UK
5. B. Gray, J. Dewynne, M. Hood, G. Wake, and R. Weber Effect of deposition of combustible matter onto electric power cables Fire Safety J. 16 6 1990 459 467
6. R. Sisson, A. Swift, G. Wake, and B. Gray The self-heating of damp cellulosic materials. II. On the steady states of the spatially distributed case IMA J. Appl. Math. 50 3 1993 285 306 (Pubitemid 23694934)
7. A. Hastings Models of spatial spread: a synthesis Biol. Conserv. 78 1996 143 148
8. P. Ming, and J. Albrecht Integrated framework for the simulation of biological invasions in a heterogeneous landscape Trans. GIS 8 3 2004 309 334 (Pubitemid 38672930)
9. M. Kot Elements of Mathematical Ecology 2001 Cambridge University Press United Kingdom, Cambridge
10. M. Neubert, and I. Parker Projecting rates of spread for invasive species Risk Anal. 24 4 2004 817 831 (Pubitemid 39238473)
11. A. Okubo Diffusion and Ecological Problems: Mathematical Models 1980 Springer-Verlag Berlin, New York
12. M.A. Azeez, and A. Vakakis Axisymmetric transient solutions of the heat diffusion problem in layered composite media Int. J. Heat Mass Transfer 43 2000 3883 3895 (Pubitemid 30656798)
13. F. de Monte Transient heat conduction in one-dimensional composite slab: a 'natural' analytic approach Int. J. Heat Mass Transfer 43 2000 3607 3619 (Pubitemid 30605112)
14. F. de Monte An analytic approach to the unsteady heat conduction processes in one-dimensional composite media Int. J. Heat Mass Transfer 45 2002 1333 1343 (Pubitemid 34096459)
15. R. Hickson, S. Barry, and G. Mercer Critical times in multilayer diffusion. Part 1: Exact solutions Int. J. Heat Mass Transfer 52 25-26 2009 5776 5783
16. R. Hickson, S. Barry, and G. Mercer Critical times in multilayer diffusion. Part 2: Approximate solutions Int. J. Heat Mass Transfer 52 25-26 2009 5784 5791
17. X. Lu, P. Tervola, and M. Viljanen Transient analytical solution to heat conduction in composite circular cylinder Int. J. Heat Mass Transfer 49 2006 341 348 (Pubitemid 43205824)
18. G. Pontrelli, and F. de Monte Mass diffusion through two-layer porous media: an application to the drug-eluting stent Int. J. Heat Mass Transfer 50 2007 3658 3669 (Pubitemid 46680313)
19. Y. Sun, and I. Wichman On transient heat conduction in a one-dimensional composite slab Int. J. Heat Mass Transfer 47 2004 1555 1559 (Pubitemid 38070344)
20. R. Hickson, Critical Times of Heat and Mass Transport Through Multiple Layers, Ph.D. Thesis; PEMS, UNSW@ADFA; 2010. Available at: .
21. M. Kot, M. Lewis, and P. van den Driessche Dispersal data and the spread of invading organisms Ecology 77 7 1996 2027 2042
22. M. Neubert, and H. Caswell Demography and dispersal: calculation and sensitivity analysis of invasion spread for structured populations Ecology 81 6 2000 1613 1628 (Pubitemid 30446146)
23. R. Fisher The wave of advance of advantageous genes Ann. Eugenics (London) 7 1937 355 369
24. A. Kolmogorov, I. Petrovsky, and N. Piscounov Étude de l'équation de la diffusion avec croissance de la quantité de matire et son application a un problme biologique Bull. Moscow Univ. Math. Mech. 1 6 1937 1 26
25. H. Kierstead, and L. Slobodkin The size of water masses containing plankton blooms J. Mar. Res. 12 1953 141 147
26. J. Skellam Random dispersal in theoretical populations Biometrika 38 1-2 1951 196 218
27. F. de Monte, J. Beck, and D. Amos Diffusion of thermal disturbances in two-dimensional cartesian transient heat conduction Int. J. Heat Mass Transfer 51 2008 5931 5941
28. R. Hickson, S. Barry, G. Mercer, H. Sidhu, Finite difference schemes for multilayer diffusion, J. Math. Comput. Modell., submitted for publication.
29. PDE Solutions Inc., FlexPDE, Spokane Valley, Version 5. .
30. The MathWorks Inc., matlab®, Natick, Massachusetts, Version 7.5.0.338 (R2007b). .
31. R. Hickson, S. Barry, and G. Mercer Exact and numerical solutions for effective diffusivity and time lag through multiple layers ANZIAM J. (E) 49 2009 C324 C340
32. J. Beck, K. Cole, A. Haji-Sheikh, and B. Litkouhi Heat Conduction using Green's Functions 1992 Hemisphere Press Washington
33. D. Duffy Green's Functions with Applications 2001 Chapman & Hall/CRC New York
34. H. Carslaw, and J. Jaeger Conduction of Heat in Solids second ed. 1959 Oxford University Press Amen House, London
35. D. Duffy Solutions of Partial Differential Equations Blue Ridge Summit 1986 Tab Books PA
36. J. Beck, and K. Cole Improving convergence of summations in heat conduction Int. J. Heat Mass Transfer 50 2007 257 268 (Pubitemid 44709001)
37. K. Landman, and M. McGuinness Mean action time for diffusive processes J. Appl. Math. Decision Sci. 4 2 2000 125 141
38. D. Allwright, M. Blount, H. Gramberg, I. Hewitt, Reaction-diffusion Models of Decontamination, Study Group Report (ESGI 2009, Southampton), Smith Institute, 2009.
39. Maplesoft, Maple 11, Waterloo, Ontario. .
40. S. Petrovskii, and N. Shigesada Some exact solutions of a generalized Fisher equation related to the problem of biological invasion Math. Biosci. 172 2001 73 94 (Pubitemid 32845981)