Abstract:
Similarity solutions for a mathematical model for thawing in a saturated semi-infinite porous medium is considered when change of phase induces a density jump and a heat flux condition of the type -q0t-(1/2) is imposed on the fixed face x = 0. Different cases depending on physical parameters are analysed and the explicit solution is obtained if and only if an inequality for the thermal coefficient q0 is verified. An improvement for the existence of a similarity solution for the same free boundary problem with a constant temperature on the fixed face x = 0 is also obtained.
Registro:
Documento: |
Artículo
|
Título: | Similarity solutions for thawing processes with a heat flux condition at the fixed boundary |
Autor: | Lombardi, A.L.; Tarzia, D.A. |
Filiación: | Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, 1428 Buenos Aires, Argentina Universidad Austral, Paraguay, CONICET, F.C.E., Departamento de Matemática, 1950, S2000FZF, Rosario, Argentina
|
Palabras clave: | Density jump; Free boundary problems; Freezing; Phase change process; Similarity solution; Solidification; Stefan problem; Thawing processes; Boundary value problems; Density (specific gravity); Freezing; Heat flux; Mathematical models; Porous materials; Solidification; Thermal coefficient; Thawing |
Año: | 2001
|
Volumen: | 36
|
Número: | 3
|
Página de inicio: | 251
|
Página de fin: | 264
|
DOI: |
http://dx.doi.org/10.1023/A:1013963424649 |
Título revista: | Meccanica
|
Título revista abreviado: | Meccanica
|
ISSN: | 00256455
|
CODEN: | MECCB
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00256455_v36_n3_p251_Lombardi |
Referencias:
- Abramowitz, M., Stegun, I., (1972) Handbook of Mathematical Functions, , Dover, New York
- Alexiades, V., Solomon, A.D., (1993) Mathematical Modeling of Melting and Freezing Processes, , Hemisphere Publ. Corp., Washington
- Charach, Ch., Rubinstein, I., Pressure-temperature effects in planar Stefan problems with density change (1992) J. Appl. Phys., 71, pp. 1128-1137
- Crank, J., (1984) Free and Moving Boundary Problems, , Clarendon Press, Oxford
- Ding, Z., Talamucci, F., Primary frost heave: A quasi steady approach (1996) Can. Appl. Math. Quart., 4, pp. 31-63
- Fasano, A., Guan, Z., Primicerio, M., Rubinstein, I., Thawing in saturated porous media (1993) Meccanica, 28, pp. 103-109
- Fasano, A., Primicerio, M., Tarzia, D.A., Similarity solutions in a class of thawing processes (1999) Math. Models Meth. Appl. Sci., 9, pp. 1-10
- Hardy, G.H., Littlewood, J.E., Polya, G., (1934) Inequalities, , Cambridge University Press, London
- Lunardini, V.J., (1991) Heat Transfer with Freezing and Thawing, , Elsevier, Amsterdam
- Nakano, Y., Quasi-steady problems in freezing soils. I. Analysis on the steady growth of an ice layer (1990) Cold. Reg. Sci. Tech., 17, pp. 207-226
- O'Neill, K., Miller, R.D., Exploration of a rigid ice model of frost heave (1985) Water Resour. Res., 21, pp. 281-296
- Talamucci, F., Analysis of the coupled heat-mass transport in freezing porous media (1997) Survey Math. Indust., 7, pp. 93-139
- Talamucci, F., Freezing processes in saturated soils (1998) Math. Models Meth. Appl. Sci., 8, pp. 107-138
- Tarzia, D.A., An inequality for the coefficient σ of the free boundary s(t) = 2σ√t of the Neumann solution for the two-phase Stefan problem (1981) Quart. Appl. Math., 39, pp. 491-497
- Tarzia, D.A., Soluciones exactas del problema de Stefan unidimensional (1984) Cuadern. Inst. Mat. Beppo Levi, 12, pp. 5-37
- Tarzia, D.A., A bibliography on moving-free boundary problems for the heat-diffusion equation: The Stefan problem and related problems (2000) MAT - Serie A, (2). , www.austral.edu.ar/MAT-SerieA/2(2000), Rosario (with 5869 titles on the subject)
Citas:
---------- APA ----------
Lombardi, A.L. & Tarzia, D.A.
(2001)
. Similarity solutions for thawing processes with a heat flux condition at the fixed boundary. Meccanica, 36(3), 251-264.
http://dx.doi.org/10.1023/A:1013963424649---------- CHICAGO ----------
Lombardi, A.L., Tarzia, D.A.
"Similarity solutions for thawing processes with a heat flux condition at the fixed boundary"
. Meccanica 36, no. 3
(2001) : 251-264.
http://dx.doi.org/10.1023/A:1013963424649---------- MLA ----------
Lombardi, A.L., Tarzia, D.A.
"Similarity solutions for thawing processes with a heat flux condition at the fixed boundary"
. Meccanica, vol. 36, no. 3, 2001, pp. 251-264.
http://dx.doi.org/10.1023/A:1013963424649---------- VANCOUVER ----------
Lombardi, A.L., Tarzia, D.A. Similarity solutions for thawing processes with a heat flux condition at the fixed boundary. Meccanica. 2001;36(3):251-264.
http://dx.doi.org/10.1023/A:1013963424649