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Volumn 41, Issue 15, 2003, Pages 1685-1698

Explicit solutions to the one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term

Author keywords

Free boundary problem; Fusion; Moving boundary problem; Nonlinear thermal conductivity; Phase change process; Similarity solution; Solidification; Stefan problem

Indexed keywords

HEAT CONVECTION; HEAT FLUX; SOLIDIFICATION; THERMAL CONDUCTIVITY;

EID: 0038018654     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7225(03)00067-3     Document Type: Article
Times cited : (38)

References (30)
  • 1
    • 0003854442 scopus 로고
    • Mathematical modeling of melting and freezing processes
    • Washington: Taylor and Francis
    • Alexiades V., Solomon A.D. Mathematical modeling of melting and freezing processes. Hemisphere. 1983;Taylor and Francis, Washington.
    • (1983) Hemisphere
    • Alexiades, V.1    Solomon, A.D.2
  • 3
    • 0024667053 scopus 로고
    • An asymptotic solution for short-time transient heat conduction between two similar contacting bodies
    • Barber J.R. An asymptotic solution for short-time transient heat conduction between two similar contacting bodies. Int. J. Heat Mass Transfer. 32:1989;943-949.
    • (1989) Int. J. Heat Mass Transfer , vol.32 , pp. 943-949
    • Barber, J.R.1
  • 4
    • 36749115773 scopus 로고
    • On the remarkable nonlinear diffusion equation
    • Bluman G., Kumei S. On the remarkable nonlinear diffusion equation. J. Math. Phys. 21:1980;1019-1023.
    • (1980) J. Math. Phys. , vol.21 , pp. 1019-1023
    • Bluman, G.1    Kumei, S.2
  • 5
    • 0009274669 scopus 로고    scopus 로고
    • Determination of unknown thermal coefficients for Storm's-type materials through a phase-change process
    • Briozzo A.C., Natale M.F., Tarzia D.A. Determination of unknown thermal coefficients for Storm's-type materials through a phase-change process. Int. J. Non-Linear Mech. 34:1999;324-340.
    • (1999) Int. J. Non-Linear Mech. , vol.34 , pp. 324-340
    • Briozzo, A.C.1    Natale, M.F.2    Tarzia, D.A.3
  • 6
    • 0036605860 scopus 로고    scopus 로고
    • An explicit solution for an instantaneous two-phase Stefan problem with nonlinear thermal coefficients
    • Briozzo A.C., Tarzia D.A. An explicit solution for an instantaneous two-phase Stefan problem with nonlinear thermal coefficients. IMA J. Appl. Math. 67:2002;249-261.
    • (2002) IMA J. Appl. Math. , vol.67 , pp. 249-261
    • Briozzo, A.C.1    Tarzia, D.A.2
  • 7
    • 0038358852 scopus 로고
    • Non-integrability of non-linear diffusion-convection equations in two spatial dimensions
    • Broadbridge P. Non-integrability of non-linear diffusion-convection equations in two spatial dimensions. J. Phys. A: Math. Gen. 19:1986;1245-1257.
    • (1986) J. Phys. A: Math. Gen. , vol.19 , pp. 1245-1257
    • Broadbridge, P.1
  • 8
    • 0038020646 scopus 로고
    • Integrable forms of the one-dimensional flow equation for unsaturated heterogeneous porous media
    • Broadbridge P. Integrable forms of the one-dimensional flow equation for unsaturated heterogeneous porous media. J. Math. Phys., Gen. 29:1988;622-627.
    • (1988) J. Math. Phys., Gen. , vol.29 , pp. 622-627
    • Broadbridge, P.1
  • 12
    • 0034010201 scopus 로고    scopus 로고
    • Liquid phase mass transfer coefficients for bubbles growing in a pressure field: A simplified analysis
    • Coelho Pinheiro M.N. Liquid phase mass transfer coefficients for bubbles growing in a pressure field: a simplified analysis. Int. Comm. Heat Mass Transfer. 27:2000;99-108.
    • (2000) Int. Comm. Heat Mass Transfer , vol.27 , pp. 99-108
    • Coelho Pinheiro, M.N.1
  • 15
    • 0009515335 scopus 로고
    • Nonlinear diffusion problems
    • Berlin: Springer
    • Fasano A., Primicerio M. Nonlinear Diffusion Problems. Lecture Notes in Math. vol. 1224:1986;Springer, Berlin.
    • (1986) Lecture Notes in Math , vol.1224
    • Fasano, A.1    Primicerio, M.2
  • 17
    • 84934736228 scopus 로고
    • Exact solutions in nonlinear diffusion
    • Knight J.H., Philip J.R. Exact solutions in nonlinear diffusion. J. Eng. Math. 8:1974;219-227.
    • (1974) J. Eng. Math. , vol.8 , pp. 219-227
    • Knight, J.H.1    Philip, J.R.2
  • 18
    • 0000624346 scopus 로고
    • Memoire sur la solidification par refroidissement d'un globe liquide
    • Lamé G., Clapeyron B.P. Memoire sur la solidification par refroidissement d'un globe liquide. Annales Chim. Phys. 47:1831;250-256.
    • (1831) Annales Chim. Phys. , vol.47 , pp. 250-256
    • Lamé, G.1    Clapeyron, B.P.2
  • 20
    • 0034695312 scopus 로고    scopus 로고
    • Explicit solutions to the two-phase Stefan problem for Storm-type materials
    • Natale M.F., Tarzia D.A. Explicit solutions to the two-phase Stefan problem for Storm-type materials. J. Phys. A: Math. Gen. 33:2000;395-404.
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 395-404
    • Natale, M.F.1    Tarzia, D.A.2
  • 21
    • 0002111075 scopus 로고
    • General method of exact solution of the concentration-dependent diffusion equation
    • Philip R. General method of exact solution of the concentration-dependent diffusion equation. Aust. J. Phys. 13:1960;1-12.
    • (1960) Aust. J. Phys. , vol.13 , pp. 1-12
    • Philip, R.1
  • 22
    • 0025209037 scopus 로고
    • The method of the 'carry over' of integral transforms in non-linear mass and heat transfer problems
    • Polyanin A.D., Dil'man V.V. The method of the 'carry over' of integral transforms in non-linear mass and heat transfer problems. Int. J. Heat Mass Transfer. 33:1990;175-181.
    • (1990) Int. J. Heat Mass Transfer , vol.33 , pp. 175-181
    • Polyanin, A.D.1    Dil'man, V.V.2
  • 23
    • 0009273352 scopus 로고
    • Variational solutions for two nonlinear boundary-value problems for diffusion with concentration-dependent coefficients
    • Reeves R.I. Variational solutions for two nonlinear boundary-value problems for diffusion with concentration-dependent coefficients. Quart. Appl. Math. 33:1975;291-295.
    • (1975) Quart. Appl. Math. , vol.33 , pp. 291-295
    • Reeves, R.I.1
  • 24
    • 0000243558 scopus 로고
    • Application of a reciprocal transformation to a two-phase Stefan problem
    • Rogers C. Application of a reciprocal transformation to a two-phase Stefan problem. J. Phys. A: Math. Gen. 18:1985;105-109.
    • (1985) J. Phys. A: Math. Gen. , vol.18 , pp. 105-109
    • Rogers, C.1
  • 25
    • 0001543917 scopus 로고
    • On a class of moving boundary problems in non-linear heat condition: Application of a Bäcklund transformation
    • Rogers C. On a class of moving boundary problems in non-linear heat condition: application of a Bäcklund transformation. Int. J. Non-Linear Mech. 21:1986;249-256.
    • (1986) Int. J. Non-Linear Mech. , vol.21 , pp. 249-256
    • Rogers, C.1
  • 26
    • 0013349826 scopus 로고
    • On a nonlinear moving boundary problem with heterogeneity: Application of reciprocal transformation
    • Rogers C., Broadbridge P. On a nonlinear moving boundary problem with heterogeneity: application of reciprocal transformation. J. Appl. Math. Phys. (ZAMP). 39:1988;122-129.
    • (1988) J. Appl. Math. Phys. (ZAMP) , vol.39 , pp. 122-129
    • Rogers, C.1    Broadbridge, P.2
  • 27
    • 0026281795 scopus 로고
    • Exact solution for nonlinear nonhysteretic redistribution in vertical soil of finite depth
    • Sander G.C., Cunning I.F., Hogarth W.L., Parlange J.Y. Exact solution for nonlinear nonhysteretic redistribution in vertical soil of finite depth. Water Resour. Res. 27:1991;1529-1536.
    • (1991) Water Resour. Res. , vol.27 , pp. 1529-1536
    • Sander, G.C.1    Cunning, I.F.2    Hogarth, W.L.3    Parlange, J.Y.4
  • 28
    • 0000903291 scopus 로고
    • An inequality for the coefficient σ of the free boundary s(t) = 2σ √t of the Neumann solution for the two-phase Stefan problem
    • 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 Quart. Appl. Math. 39:1981;491-497.
    • (1981) Quart. Appl. Math. , vol.39 , pp. 491-497
    • Tarzia, D.A.1
  • 29
    • 0242357322 scopus 로고    scopus 로고
    • A bibliography on moving-free boundary problems for the heat diffusion equation
    • Rosario, with 5869 titles on the subject
    • D.A. Tarzia, A bibliography on moving-free boundary problems for the heat diffusion equation. The Stefan problem, MAT- Serie A, Rosario, vol. 2, 2000, with 5869 titles on the subject, 300pp. See www.austral.edu.ar/MAT-SerieA/2 (2000)/.
    • (2000) The Stefan Problem, MAT- Serie A , vol.2 , pp. 300
    • Tarzia, D.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.