DOI: 10.1139/p59-037. THE TRANSPORT OF HEAT BETWEEN DISSIMILAR SOLIDS AT LOW TEMPERATURES

THE TRANSPORT OF HEAT BETWEEN DISSIMILAR SOLIDS AT LOW TEMPERATURES

10.1139/p59-037

Crossref journal-article

Canadian Science Publishing

Canadian Journal of Physics (155)

Abstract

The resistance offered to the flow of heat by the mismatch of the elastic constants at the interface between two materials has been calculated. It is shown that for a perfectly joined interface the heat flow is proportional to the difference of the fourth powers of the temperature on each side of the interface. Deviations from this temperature dependence are to be expected for rough surfaces and for surfaces pressed into contact with one another. The calculated contact resistance between some common solids is given, and graphs are presented from which the heat flow between any two materials may be computed. It is shown too that the spin–phonon, phonon–electron, and phonon–phonon relaxation processes give rise to additional resistive processes in some solids, some of which restrict the heat flow at the surface. The theoretical results compare well with the available experimental data. However, the problem of the contact resistance between helium and metals is still unresolved. A tentative explanation of this is presented which predicts that there should be an appreciable difference between the contact resistance of a metal in the normal and in the superconducting state.

Bibliography

Little, W. A. (1959). THE TRANSPORT OF HEAT BETWEEN DISSIMILAR SOLIDS AT LOW TEMPERATURES. Canadian Journal of Physics, 37(3), 334â349.

Authors 1

W. A. Little (first)

References 14 Referenced 803

AMBLER,E. 1953. Thesis, University of Oxford.
10.1063/1.1722369 / J. Appl. Phys. by BERMAN R. (1956)
FAIRBANK.H. A. and LEE. D. M. 1957. The Fifth International Conference of Low e k e r a t u r es Physics and Chemistry, Wisconsin.
{'key': 'p_4/p_4_1', 'first-page': '545', 'volume': '231', 'author': 'FAIRBANK H. A.', 'year': '1955', 'journal-title': 'Roy. Soc. (London), A'} / Roy. Soc. (London), A by FAIRBANK H. A. (1955)
10.1088/0370-1298/66/3/303 / Phvs. Soc. (London). A. by GOODMAN B. B. (1953)
10.1016/0031-8914(51)90109-7 / Physica by GORTER C. J. (1951)
{'key': 'p_7/p_7_1', 'first-page': '181', 'volume': '4', 'author': 'KAPITZA P. L.', 'year': '1941', 'journal-title': 'Phys. (U.S.S.R.)'} / Phys. (U.S.S.R.) by KAPITZA P. L. (1941)
{'key': 'p_8/p_8_1', 'first-page': '687', 'volume': '22', 'author': 'KHALATNIKOV I. M.', 'year': '1952', 'journal-title': 'Exptl. Theoret. Phys. (U.S.S.R.)'} / Exptl. Theoret. Phys. (U.S.S.R.) by KHALATNIKOV I. M. (1952)
KOLSKY,H. 1953. Stress waves in solids (Oxford-University Press, Londot).
KRONIG,R. and THELLUNG,A. 1950. Physica, 16, 678. (10.1016/0031-8914(50)90036-X)
MIEDEMA.A. R. POSTMA.H. and STEENLAND.M. of LOW & n e r a t u ;ePhysics. 1958. KarnerlinchOnnes Conference -
RAYLEIGH,LORD. 1894. Theory of sound (Macmillan & Co., Ltd., London).
10.1103/PhysRev.110.65 / Phys. Rev. by STRANDBERG M. W. (1958)
\\IILSON,A. H. 1953. The theory of metals (Cambridge University Press, London).

Dates

Type	When
Created	14 years, 3 months ago (April 24, 2011, 3:29 a.m.)
Deposited	1 month, 2 weeks ago (July 2, 2025, 10:39 a.m.)
Indexed	2 weeks, 5 days ago (Aug. 2, 2025, 1:23 a.m.)
Issued	66 years, 5 months ago (March 1, 1959)
Published	66 years, 5 months ago (March 1, 1959)
Published Print	66 years, 5 months ago (March 1, 1959)

Funders 0

None

BibTeX

@article{Little_1959, title={THE TRANSPORT OF HEAT BETWEEN DISSIMILAR SOLIDS AT LOW TEMPERATURES}, volume={37}, ISSN={1208-6045}, url={http://dx.doi.org/10.1139/p59-037}, DOI={10.1139/p59-037}, number={3}, journal={Canadian Journal of Physics}, publisher={Canadian Science Publishing}, author={Little, W. A.}, year={1959}, month=mar, pages={334–349} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        2
      ]
    ],
    "date-time": "2025-08-02T05:23:29Z",
    "timestamp": 1754112209580,
    "version": "3.41.0"
  },
  "reference-count": 14,
  "publisher": "Canadian Science Publishing",
  "issue": "3",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1959,
            3,
            1
          ]
        ],
        "date-time": "1959-03-01T00:00:00Z",
        "timestamp": -342057600000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "http://www.nrcresearchpress.com/page/about/CorporateTextAndDataMining"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1959,
        3,
        1
      ]
    ]
  },
  "abstract": "<jats:p> The resistance offered to the flow of heat by the mismatch of the elastic constants at the interface between two materials has been calculated. It is shown that for a perfectly joined interface the heat flow is proportional to the difference of the fourth powers of the temperature on each side of the interface. Deviations from this temperature dependence are to be expected for rough surfaces and for surfaces pressed into contact with one another. The calculated contact resistance between some common solids is given, and graphs are presented from which the heat flow between any two materials may be computed. It is shown too that the spin\u2013phonon, phonon\u2013electron, and phonon\u2013phonon relaxation processes give rise to additional resistive processes in some solids, some of which restrict the heat flow at the surface. The theoretical results compare well with the available experimental data. However, the problem of the contact resistance between helium and metals is still unresolved. A tentative explanation of this is presented which predicts that there should be an appreciable difference between the contact resistance of a metal in the normal and in the superconducting state. </jats:p>",
  "DOI": "10.1139/p59-037",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2011,
        4,
        24
      ]
    ],
    "date-time": "2011-04-24T07:29:26Z",
    "timestamp": 1303630166000
  },
  "page": "334-349",
  "source": "Crossref",
  "is-referenced-by-count": 803,
  "title": "THE TRANSPORT OF HEAT BETWEEN DISSIMILAR SOLIDS AT LOW TEMPERATURES",
  "prefix": "10.1139",
  "volume": "37",
  "author": [
    {
      "given": "W. A.",
      "family": "Little",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "155",
  "reference": [
    {
      "key": "p_1/p_1_1",
      "unstructured": "AMBLER,E. 1953. Thesis, University of Oxford."
    },
    {
      "key": "p_2/p_2_1",
      "doi-asserted-by": "crossref",
      "first-page": "318",
      "DOI": "10.1063/1.1722369",
      "volume": "27",
      "author": "BERMAN R.",
      "year": "1956",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "p_3/p_3_1",
      "unstructured": "FAIRBANK.H. A. and LEE. D. M. 1957. The Fifth International Conference of Low e k e r a t u r es Physics and Chemistry, Wisconsin."
    },
    {
      "key": "p_4/p_4_1",
      "first-page": "545",
      "volume": "231",
      "author": "FAIRBANK H. A.",
      "year": "1955",
      "journal-title": "Roy. Soc. (London), A"
    },
    {
      "key": "p_5/p_5_1",
      "doi-asserted-by": "crossref",
      "first-page": "217",
      "DOI": "10.1088/0370-1298/66/3/303",
      "volume": "66",
      "author": "GOODMAN B. B.",
      "year": "1953",
      "journal-title": "Phvs. Soc. (London). A."
    },
    {
      "key": "p_6/p_6_1",
      "doi-asserted-by": "crossref",
      "first-page": "841",
      "DOI": "10.1016/0031-8914(51)90109-7",
      "volume": "17",
      "author": "GORTER C. J.",
      "year": "1951",
      "journal-title": "Physica"
    },
    {
      "key": "p_7/p_7_1",
      "first-page": "181",
      "volume": "4",
      "author": "KAPITZA P. L.",
      "year": "1941",
      "journal-title": "Phys. (U.S.S.R.)"
    },
    {
      "key": "p_8/p_8_1",
      "first-page": "687",
      "volume": "22",
      "author": "KHALATNIKOV I. M.",
      "year": "1952",
      "journal-title": "Exptl. Theoret. Phys. (U.S.S.R.)"
    },
    {
      "key": "p_9/p_9_1",
      "unstructured": "KOLSKY,H. 1953. Stress waves in solids (Oxford-University Press, Londot)."
    },
    {
      "key": "p_10/p_10_1",
      "doi-asserted-by": "crossref",
      "unstructured": "KRONIG,R. and THELLUNG,A. 1950. Physica, 16, 678.",
      "DOI": "10.1016/0031-8914(50)90036-X"
    },
    {
      "key": "p_11/p_11_1",
      "unstructured": "MIEDEMA.A. R. POSTMA.H. and STEENLAND.M. of LOW & n e r a t u ;ePhysics. 1958. KarnerlinchOnnes Conference -"
    },
    {
      "key": "p_12/p_12_1",
      "unstructured": "RAYLEIGH,LORD. 1894. Theory of sound (Macmillan & Co., Ltd., London)."
    },
    {
      "key": "p_13/p_13_1",
      "doi-asserted-by": "crossref",
      "first-page": "65",
      "DOI": "10.1103/PhysRev.110.65",
      "volume": "110",
      "author": "STRANDBERG M. W.",
      "year": "1958",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "p_14/p_14_1",
      "unstructured": "\\\\IILSON,A. H. 1953. The theory of metals (Cambridge University Press, London)."
    }
  ],
  "container-title": "Canadian Journal of Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://cdnsciencepub.com/doi/pdf/10.1139/p59-037",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2025,
        7,
        2
      ]
    ],
    "date-time": "2025-07-02T14:39:34Z",
    "timestamp": 1751467174000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://cdnsciencepub.com/doi/10.1139/p59-037"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1959,
        3,
        1
      ]
    ]
  },
  "references-count": 14,
  "journal-issue": {
    "issue": "3",
    "published-print": {
      "date-parts": [
        [
          1959,
          3,
          1
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1139/p59-037"
  ],
  "URL": "http://dx.doi.org/10.1139/p59-037",
  "relation": {},
  "ISSN": [
    "0008-4204",
    "1208-6045"
  ],
  "subject": [],
  "container-title-short": "Can. J. Phys.",
  "published": {
    "date-parts": [
      [
        1959,
        3,
        1
      ]
    ]
  }
}