Some thermodynamical aspects of the solidification of two-phase flows

Meccanica

Volumn 39, Issue 4, 2004, Pages 369-382

  Mariano, Paolo Maria ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Mixtures; Multifield theories; Stefan problem; Two phase flows

Indexed keywords

ALUMINA; ENERGY DISSIPATION; EQUATIONS OF MOTION; FRICTION; HEAT FLUX; INTERFACIAL ENERGY; MATHEMATICAL MODELS; MICROSTRUCTURE; PHASE TRANSITIONS; PROBLEM SOLVING; SOLIDIFICATION; STEEL CASTINGS; STRESSES; THERMODYNAMICS; VECTORS;

KINETIC STRESSES; MULTIFIELD THEORIES; PHASE SELECTION; STEFAN PROBLEMS;

TWO PHASE FLOW;

EID: 3042846782     PISSN: 00256455     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:MECC.0000029388.33873.bd     Document Type: Article

References (20)

1. Fasano, A. and Primicerio, M., 'Il problema di Stefan con condizioni al contomo non-lineari', Ann. Scuola Norm. Sup. Pisa 26 (1972) 711-737.
2. Drew, D.A., 'Two-phase flows: constitutive equations for lift and Brownian motion and some basic flows', Arch. Ration. Mech. Anal. 62 (1976) 149-163.
3. Drew, D.A., 'Continuum modeling of two-phase flows', in: Theory of Dispersed Multiphase Flow, Academic Press, New York, 1983, pp. 173-190.
4. Drew, D.A. and Passman, S.L., Theory of Multiconstituent Fluids, Springer-Verlag, Berlin, 1999.
5. Drumheller, D.S. and Bedford, A.S., 'A thermomechanical theory for reacting immiscible mixtures', Arch. Ration. Mech. Anal. 73 (1980) 257-284.
6. Ramshaw, J.D., 'Brownian motion in multiphase flow', Theoret. Comput. Fluid Dyn. 14 (2000) 195-202.
7. Boettinger, W.J., Coriell, S.R., Greer, A.L., Karma, A., Kurtz, W., Rappaz, M. and Trivedi, R., 'Solidification microstructures: recent developments, future directions', Acta Mater. 48 (2000) 43-70.
8. Truesdell, C.A., Rational Thermodynamics, Springer-Verlag, Berlin, 1984.
9. Capriz, G., 'Continua with latent microstructure', Arch. Ration. Mech. Anal. 90 (1985) 43-56.
10. Capriz, G., Continua with Microstructure, Springer-Verlag, Berlin, 1989.
11. Nunziato, J.W. and Walsh, E.K., 'On ideal multiphase mixtures with chemical reaction and diffusion', Arch. Ration. Mech. Anal. 73 (1980) 285-311.
12. Passman, S.L., Nunziato, J.W. and Walsh, E.K., 'A theory of multiphase mixtures', in: Truesdell, C.A. (ed), Rational Thermodynamics, Springer-Verlag, Berlin, 1984.
13. Gurtin, M.E., Polignone, D. and Vinals, J., 'Two-phase binary fluids and immiscible fluids described by an order parameter', Math. Models Methods Appl. Sci. 6 (1996) 815-831.
14. Antman, S.S., 'Physically unacceptable viscous stresses', Z. Angew. Math. Phys. ZAMP 49 (1998) 980-988.
15. Šilhavý, M., The Mechanics and Thermodynamics of Continuous Media, Springer-Verlag, Berlin, 1997.
16. Baldoni, F. and Rajagopal, K.R., 'A continuum theory for the thermomechanics of solidification', Int. J. Non-Linear Mech. 32 (1997) 3-20.
17. Fried, E. and Shen, A.Q., 'Generalization of the Stefan model to allow for both velocity and temperature jumps', Cont. Mech. Thermodyn. 11 (1999) 277-296.
18. Abeyaratne, R. and Knowles, J.K., 'On the driving traction acting on a surface of strain discontinuity in a continuum', J. Mech. Phys. Solids 38 (1990) 345-360.
19. Caginalp, G., 'Penrose-Fife modification of solidification equations has no freezing or melting', Appl. Math. Lett. 5 (1992) 93-96.
20. Mariano, P.M., 'Multifield theories in mechanics of solids', Adv. Appl. Mech. 38 (2001) 1-93.