Fractional Stefan problems exhibiting lumped and distributed latent-heat memory effects

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 87, Issue 4, 2013, Pages

  Voller, Vaughan R ^a   Falcini, Federico ^b   Garra, Roberto ^c  

^a University of Minnesota   (United States)

^b CNR   (Italy)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSE INTERFACE; DIFFUSE-INTERFACE MODELS; LIQUID PHASE; MELTING PROBLEM; MEMORY EFFECTS; SHARP INTERFACE; SOLID PHASIS; STEFAN PROBLEM;

LIQUIDS;

PHASE INTERFACES;

EID: 84876722376     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.87.042401     Document Type: Article

References (23)

1. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Clarendon, Oxford, 1959).
2. J. Crank, Free and Moving Boundary Problems (Clarendon, Oxford, 1984).
3. C. M. Elliott and J. R. Ockendon, Weak and Variational Methods for Moving Boundary Problems (Pittman, Boston, 1982).
4. V. R. Voller, J. Comput. Phys. JCTPAH 0021-9991 10.1016/j.jcp.2004.04.009 200, 399 (2004). (Pubitemid 39435993)
5. J. A. Luoma and V. R. Voller, Appl. Math. Model. AMMODL 0307-904X 10.1016/S0307-904X(00)00004-4 24, 575 (2000). (Pubitemid 30411415)
6. R. H. Price and M. R. Slack, Br. J. Appl. Phys. BJAPAJ 0508-3443 10.1088/0508-3443/5/8/304 5, 285 (1954).
7. W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, Annu. Rev. Mater. Res. ARMRCU 1531-7331 10.1146/annurev.matsci.32.101901.155803 32, 163 (2002). (Pubitemid 34992569)
8. G. Caginalp, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.39.5887 39, 5887 (1989).
9. M. Fabbri and V. R. Voller, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1996.5585 130, 256 (1997). (Pubitemid 127170572)
10. R. Schumer, M. M. Meerschaert, and B. Baeumer, J. Geophys. Res. 0148-0227 10.1029/2008JF001246 114, F00A07 (2009).
11. R. Schumer, D. A. Benson, M. M. Meerschaert, and S. W. Wheatcraft, J. Contam. Hydrol. JCOHE6 0169-7722 10.1016/S0169-7722(00)00170-4 48, 69 (2001). (Pubitemid 32141059)
12. Y. Zhang, D. A. Benson, and D. M. Reeves, Adv. Water Resour. AWREDI 0309-1708 10.1016/j.advwatres.2009.01.008 32, 561 (2009).
13. E. Gerolymatou, I. Vardoulakis, and R. Hilfer, J. Phys. D JPAPBE 0022-3727 10.1088/0022-3727/39/18/022 39, 4104 (2006). (Pubitemid 44335713)
14. M. Küntz and P. Lavallée, J. Phys. D JPAPBE 0022-3727 10.1088/0022-3727/34/16/322 34, 2547 (2001). (Pubitemid 32796831)
15. A. E.-G. El Abd and J. J. Milczarek, J. Phys. D JPAPBE 0022-3727 10.1088/0022-3727/37/16/013 37, 2305 (2004).
16. D. A. Lockington and J-Y Parlange, J. Phys. D JPAPBE 0022-3727 10.1088/0022-3727/36/6/320 36, 760 (2003).
17. D. N. Gerasimov, V. A. Kondratieva, and O. A. Sinkevich, Physica D PDNPDT 0167-2789 10.1016/j.physd.2010.04.005 239, 1593 (2010).
18. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of Their Applications (Academic, San Diego, 1999).
19. J. Liu and M. Xu, J. Math. Anal. Appl. JMANAK 0022-247X 10.1016/j.jmaa.2008.10.042 351, 536 (2009).
20. V. R. Voller, Int. J. Heat Mass Transf. IJHMAK 0017-9310 10.1016/j.ijheatmasstransfer.2010.07.038 53, 5622 (2010).
21. J. A. Dantsig and M. Rappaz, Solidification (EPFL, Lausanne, 2010).
22. J. H. Cushman and T. R. Ginn, Water Resour. Res. WRERAQ 0043-1397 10.1029/2000WR900261 36, 3763 (2000). (Pubitemid 32039925)
23. R. Metzler and J. Klafter, Phys. Rep. 0370-1573 10.1016/S0370-1573(00) 00070-3 339, 1 (2000).