Heat conduction in two-dimensional parquets and optimization of spine shape

Anvar Kassimov, Yurii V. Obnosov

Research output: Contribution to journalConference article

3 Citations (Scopus)

Abstract

By the methods of complex analysis media composed of double- periodic phases with different (arbitrary) conductivity are considered. Within each phase temperature is a harmonic function and along interfaces two conjugation conditions are rigorously satisfied (continuity of temperature and normal flux component) as well as periodicity conditions along the boundaries of elementary cells. For specific examples of composites (lensed structure and chequer-board) explicit analytic solutions are derived in terms of the thermogradients. The effective conductivities are calculated. For the chequer-board composite the hodograph of effective conductivity absolute value is shown to coincide exactly with an ellipse. As a limiting case of parquets developed surfaces are studied. In the class of semi-ellipsoidal spines two non-trivial local extrema of the total flux exist alongside two global ones. Both for two-dimensional and three-dimensional protrusions these extrema appear if the conductivity ratio exceeds some critical value.

Fingerprint

spine
Heat conduction
conductive heat transfer
Fluxes
Harmonic functions
conductivity
optimization
range (extremes)
Composite structures
hodographs
harmonic functions
Temperature
Composite materials
composite structures
ellipses
conjugation
continuity
periodic variations
composite materials
temperature

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Mechanical Engineering
  • Condensed Matter Physics
  • Computer Science Applications

Cite this

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title = "Heat conduction in two-dimensional parquets and optimization of spine shape",
abstract = "By the methods of complex analysis media composed of double- periodic phases with different (arbitrary) conductivity are considered. Within each phase temperature is a harmonic function and along interfaces two conjugation conditions are rigorously satisfied (continuity of temperature and normal flux component) as well as periodicity conditions along the boundaries of elementary cells. For specific examples of composites (lensed structure and chequer-board) explicit analytic solutions are derived in terms of the thermogradients. The effective conductivities are calculated. For the chequer-board composite the hodograph of effective conductivity absolute value is shown to coincide exactly with an ellipse. As a limiting case of parquets developed surfaces are studied. In the class of semi-ellipsoidal spines two non-trivial local extrema of the total flux exist alongside two global ones. Both for two-dimensional and three-dimensional protrusions these extrema appear if the conductivity ratio exceeds some critical value.",
author = "Anvar Kassimov and Obnosov, {Yurii V.}",
year = "1997",
month = "1",
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doi = "10.1615/ICHMT.1997.IntSymLiqTwoPhaseFlowTranspPhenCHT.660",
language = "English",
journal = "International Symposium on Advances in Computational Heat Transfer",
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T1 - Heat conduction in two-dimensional parquets and optimization of spine shape

AU - Kassimov, Anvar

AU - Obnosov, Yurii V.

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N2 - By the methods of complex analysis media composed of double- periodic phases with different (arbitrary) conductivity are considered. Within each phase temperature is a harmonic function and along interfaces two conjugation conditions are rigorously satisfied (continuity of temperature and normal flux component) as well as periodicity conditions along the boundaries of elementary cells. For specific examples of composites (lensed structure and chequer-board) explicit analytic solutions are derived in terms of the thermogradients. The effective conductivities are calculated. For the chequer-board composite the hodograph of effective conductivity absolute value is shown to coincide exactly with an ellipse. As a limiting case of parquets developed surfaces are studied. In the class of semi-ellipsoidal spines two non-trivial local extrema of the total flux exist alongside two global ones. Both for two-dimensional and three-dimensional protrusions these extrema appear if the conductivity ratio exceeds some critical value.

AB - By the methods of complex analysis media composed of double- periodic phases with different (arbitrary) conductivity are considered. Within each phase temperature is a harmonic function and along interfaces two conjugation conditions are rigorously satisfied (continuity of temperature and normal flux component) as well as periodicity conditions along the boundaries of elementary cells. For specific examples of composites (lensed structure and chequer-board) explicit analytic solutions are derived in terms of the thermogradients. The effective conductivities are calculated. For the chequer-board composite the hodograph of effective conductivity absolute value is shown to coincide exactly with an ellipse. As a limiting case of parquets developed surfaces are studied. In the class of semi-ellipsoidal spines two non-trivial local extrema of the total flux exist alongside two global ones. Both for two-dimensional and three-dimensional protrusions these extrema appear if the conductivity ratio exceeds some critical value.

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