메뉴 건너뛰기




Volumn 29, Issue 13, 2006, Pages 1599-1613

On the heat flux vector for flowing granular materials - Part II: Derivation and special cases

Author keywords

Conduction; Constitutive relation; Fourier's law; Granular materials; Heat flux vector

Indexed keywords

CONTINUUM MECHANICS; GRANULAR MATERIALS; HEAT CONDUCTION; HEAT FLUX; HEAT TRANSFER; KINEMATICS; POROUS MATERIALS;

EID: 33747100734     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.745     Document Type: Article
Times cited : (31)

References (66)
  • 8
    • 0005754680 scopus 로고
    • The rheology of powders
    • Edwards SF. The rheology of powders. Rheologica Acta 1990; 29:493-499.
    • (1990) Rheologica Acta , vol.29 , pp. 493-499
    • Edwards, S.F.1
  • 9
    • 0031171163 scopus 로고    scopus 로고
    • A fluid mechanistic approach to slow, factional flow of powders
    • Tardos GI. A fluid mechanistic approach to slow, factional flow of powders. Powder Technology 1997; 92: 61-74.
    • (1997) Powder Technology , vol.92 , pp. 61-74
    • Tardos, G.I.1
  • 10
    • 0005703968 scopus 로고
    • Experiments showing dilatancy a property of granular material, possibly connected with gravitation
    • Reynolds O. Experiments showing dilatancy a property of granular material, possibly connected with gravitation. Proceedings of the Royal Institute of Great Britain 1886; 11:356-363.
    • (1886) Proceedings of the Royal Institute of Great Britain , vol.11 , pp. 356-363
    • Reynolds, O.1
  • 11
    • 0002902651 scopus 로고
    • Experiments on a gravity free dispersion of large solid spheres in a Newtonian fluid under shear
    • Bagnold RA. Experiments on a gravity free dispersion of large solid spheres in a Newtonian fluid under shear. Proceedings of the Royal Society of London, Series A 1954; 225:49-63.
    • (1954) Proceedings of the Royal Society of London, Series A , vol.225 , pp. 49-63
    • Bagnold, R.A.1
  • 12
    • 0009748636 scopus 로고
    • Rheology
    • Flugge S (ed.). Springer: Berlin
    • Reiner M. Rheology. In Handbuch Der Physik, Flugge S (ed.). Springer: Berlin, 1958.
    • (1958) Handbuch der Physik
    • Reiner, M.1
  • 13
  • 15
    • 0035677117 scopus 로고    scopus 로고
    • A continuum model for granular materials: Considering dilatancy, and the MohrCoulomb criterion
    • Massoudi M, Mehrabadi MM. A continuum model for granular materials: considering dilatancy, and the MohrCoulomb criterion. Acta Mechanica 2001; 152:121-138.
    • (2001) Acta Mechanica , vol.152 , pp. 121-138
    • Massoudi, M.1    Mehrabadi, M.M.2
  • 16
    • 0016026415 scopus 로고
    • A theory for the flow of granular materials
    • Cowin SC. A theory for the flow of granular materials. Powder Technology 1974; 9:61-69.
    • (1974) Powder Technology , vol.9 , pp. 61-69
    • Cowin, S.C.1
  • 17
    • 0035372796 scopus 로고    scopus 로고
    • A continuum-kinetic theory approach to the flow of granular materials: The effects of volume fraction gradient
    • Massoudi M, Boyle EJ. A continuum-kinetic theory approach to the flow of granular materials: the effects of volume fraction gradient. International Journal of Non-Linear Mechanics 2001; 36:637-648.
    • (2001) International Journal of Non-linear Mechanics , vol.36 , pp. 637-648
    • Massoudi, M.1    Boyle, E.J.2
  • 18
    • 0001686317 scopus 로고    scopus 로고
    • Origin of normal stress differences in rapid granular flows
    • Goldhirsch I, Sela N. Origin of normal stress differences in rapid granular flows. Physical Review E 1996; 54:4458-4461.
    • (1996) Physical Review E , vol.54 , pp. 4458-4461
    • Goldhirsch, I.1    Sela, N.2
  • 21
    • 0032292645 scopus 로고    scopus 로고
    • Reflections on the mechanics of granular matter
    • de Gennes PG. Reflections on the mechanics of granular matter. Physica A 1998; 261:267-293.
    • (1998) Physica A , vol.261 , pp. 267-293
    • De Gennes, P.G.1
  • 23
    • 31144432303 scopus 로고    scopus 로고
    • Constitutive modelling of flowing granular materials: A continuum approach
    • Antony SJ, Hoyle W, Ding Y (eds). The Royal Society of Chemistry: Cambridge, U.K.
    • Massoudi M. Constitutive modelling of flowing granular materials: a continuum approach. In Granular Materials: Fundamentals and Applications, Antony SJ, Hoyle W, Ding Y (eds). The Royal Society of Chemistry: Cambridge, U.K., 2004; 63-107.
    • (2004) Granular Materials: Fundamentals and Applications , pp. 63-107
    • Massoudi, M.1
  • 29
    • 0035469834 scopus 로고    scopus 로고
    • Early study of heat transfer: Newton and Fourier
    • Winterton RHS. Early study of heat transfer: Newton and Fourier. Heat Transfer Engineering 2001; 22:3-11.
    • (2001) Heat Transfer Engineering , vol.22 , pp. 3-11
    • Winterton, R.H.S.1
  • 34
    • 0000172887 scopus 로고
    • Second sound in solids
    • Chester M. Second sound in solids. Physical Review 1963; 131:2013-2015.
    • (1963) Physical Review , vol.131 , pp. 2013-2015
    • Chester, M.1
  • 37
    • 0029204135 scopus 로고
    • Nonclassical thermal effects in Stokes' second problem
    • Puri P, Kythe PK. Nonclassical thermal effects in Stokes' second problem, Acta Mechanica 1995; 112:1-9.
    • (1995) Acta Mechanica , vol.112 , pp. 1-9
    • Puri, P.1    Kythe, P.K.2
  • 38
    • 0031103848 scopus 로고    scopus 로고
    • Discontinuities in velocity gradients and temperature in the Stokes' first problem with nonclassical heat conduction
    • Puri P, Kythe PK. Discontinuities in velocity gradients and temperature in the Stokes' first problem with nonclassical heat conduction. Quarterly of Applied Mathematics 1997; 55:167-176,
    • (1997) Quarterly of Applied Mathematics , vol.55 , pp. 167-176
    • Puri, P.1    Kythe, P.K.2
  • 40
    • 0032663344 scopus 로고    scopus 로고
    • Fourier's law of heat conduction in a non-linear fluid
    • Jaric J, Golubovic Z. Fourier's law of heat conduction in a non-linear fluid. Journal of Thermal Stresses 1999; 22:293-303.
    • (1999) Journal of Thermal Stresses , vol.22 , pp. 293-303
    • Jaric, J.1    Golubovic, Z.2
  • 41
    • 0035423744 scopus 로고    scopus 로고
    • Vector-field theory of heat flux in convective heat transfer
    • Wang L. Vector-field theory of heat flux in convective heat transfer. Nonlinear Analysis 2001; 47:5009-5020.
    • (2001) Nonlinear Analysis , vol.47 , pp. 5009-5020
    • Wang, L.1
  • 43
    • 31144434122 scopus 로고    scopus 로고
    • An anisotropic constitutive relation for the stress tensor of a rod-like (fibrous-type) granular material
    • Massoudi M. An anisotropic constitutive relation for the stress tensor of a rod-like (fibrous-type) granular material. Mathematical Problems in Engineering 2005; 679-702.
    • (2005) Mathematical Problems in Engineering , pp. 679-702
    • Massoudi, M.1
  • 44
    • 0002632693 scopus 로고
    • The mechanism of fabric change during compressional deformation of sand
    • Oda M. The mechanism of fabric change during compressional deformation of sand. Soils and Foundations 1972; 12:1-18.
    • (1972) Soils and Foundations , vol.12 , pp. 1-18
    • Oda, M.1
  • 45
    • 0022097744 scopus 로고
    • The relationship between the elasticity tensor and the fabric tensor
    • Cowin SC. The relationship between the elasticity tensor and the fabric tensor. Mechanics of Materials 1985; 4:137-147.
    • (1985) Mechanics of Materials , vol.4 , pp. 137-147
    • Cowin, S.C.1
  • 47
    • 0021555989 scopus 로고
    • Micromechanically based rate constitutive description for granular materials
    • Desai CS, Gallagher RH (eds). Wiley: New York
    • Nemat-Nasser S, Mehrabadi MM. Micromechanically based rate constitutive description for granular materials. In Mechanics of Engineering Materials, Desai CS, Gallagher RH (eds). Wiley: New York, 1984; 451-463.
    • (1984) Mechanics of Engineering Materials , pp. 451-463
    • Nemat-Nasser, S.1    Mehrabadi, M.M.2
  • 48
    • 85012620788 scopus 로고
    • Consideration on the stress-dilatancy equation through the work increment tensor
    • Satake M, Jenkins JT (eds). Elsevier
    • Satake M. Consideration on the stress-dilatancy equation through the work increment tensor. In Micromechanics of Granular Materials, Satake M, Jenkins JT (eds). Elsevier, 1988; 61-70.
    • (1988) Micromechanics of Granular Materials , pp. 61-70
    • Satake, M.1
  • 49
    • 0037235450 scopus 로고    scopus 로고
    • Double-shearing theory applied to instability and strain localization in granular materials
    • Spencer AJM. Double-shearing theory applied to instability and strain localization in granular materials. Journal of Engineering Mathematics 2003; 45:55-74.
    • (2003) Journal of Engineering Mathematics , vol.45 , pp. 55-74
    • Spencer, A.J.M.1
  • 50
    • 0001314297 scopus 로고
    • A mathematical theory of dilatancy
    • Reiner M. A mathematical theory of dilatancy. American Journal of Mathematics 1945; 67:350-362.
    • (1945) American Journal of Mathematics , vol.67 , pp. 350-362
    • Reiner, M.1
  • 51
    • 0004143097 scopus 로고
    • A method for measuring material moduli for granular materials: Flow in an orthogonal rheometer
    • DOE/PETC/TR90/3, US Department of Energy, Pittsburgh
    • Rajagopal KR, Massoudi M. A method for measuring material moduli for granular materials: flow in an orthogonal rheometer. Topical Report, DOE/PETC/TR90/3, US Department of Energy, Pittsburgh, 1990.
    • (1990) Topical Report
    • Rajagopal, K.R.1    Massoudi, M.2
  • 52
    • 17844400597 scopus 로고    scopus 로고
    • Conservation laws and constitutive relations for density-gradient- dependent viscous fluids
    • Mehrabadi MM, Cowin SC, Massoudi M. Conservation laws and constitutive relations for density-gradient-dependent viscous fluids. Continuum Mechanics and Thermodynamics 2005; 17:183-200.
    • (2005) Continuum Mechanics and Thermodynamics , vol.17 , pp. 183-200
    • Mehrabadi, M.M.1    Cowin, S.C.2    Massoudi, M.3
  • 55
    • 0001416793 scopus 로고
    • Theory of invariants
    • Bringen AC (ed.). Academic Press: New York
    • Spencer AJM. Theory of invariants. In Continuum Physics, Bringen AC (ed.), vol I. Academic Press: New York, 1971.
    • (1971) Continuum Physics , vol.1
    • Spencer, A.J.M.1
  • 56
    • 85025220892 scopus 로고
    • Theory of representations for tensor functions - A unified invariant approach to constitutive equations
    • Zheng QS. Theory of representations for tensor functions - a unified invariant approach to constitutive equations. Applied Mechanics Reviews 1994; 47:545-587.
    • (1994) Applied Mechanics Reviews , vol.47 , pp. 545-587
    • Zheng, Q.S.1
  • 60
    • 0022138260 scopus 로고
    • Forces on the solid constituent in a multiphase flow
    • Passman SL. Forces on the solid constituent in a multiphase flow. Journal of Rheology 1986; 30:1077-1083.
    • (1986) Journal of Rheology , vol.30 , pp. 1077-1083
    • Passman, S.L.1
  • 61
    • 0032966943 scopus 로고    scopus 로고
    • Fourier's heat conduction equation: History, influence, and connections
    • Narasimhan TN. Fourier's heat conduction equation: history, influence, and connections. Reviews of Geophysics 1999; 37:151-172.
    • (1999) Reviews of Geophysics , vol.37 , pp. 151-172
    • Narasimhan, T.N.1
  • 62
    • 0000872238 scopus 로고    scopus 로고
    • Departures from Fourier's law for fluidized granular media
    • Soto R, Mareschal M, Risso D. Departures from Fourier's law for fluidized granular media. Physical Review Letters 1999; 83:5003-5006.
    • (1999) Physical Review Letters , vol.83 , pp. 5003-5006
    • Soto, R.1    Mareschal, M.2    Risso, D.3
  • 66
    • 0035394571 scopus 로고    scopus 로고
    • Modeling anisotropic fluids within the framework of bodies with multiple natural configurations
    • Rajagopal KR, Srinivasa AR. Modeling anisotropic fluids within the framework of bodies with multiple natural configurations. Journal of Non-Newtonian Fluid Mechanics 2001; 99:109-124.
    • (2001) Journal of Non-newtonian Fluid Mechanics , vol.99 , pp. 109-124
    • Rajagopal, K.R.1    Srinivasa, A.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.