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Characterization of Thermal Transport in One-dimensional Solid Materials
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Non-steady-state heat conduction in composite walls.

Bernard Deconinck1, Beatrice Pelloni2, Natalie E Sheils1

  • 1Department of Applied Mathematics , University of Washington , Seattle, WA 98195-2420, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|May 9, 2014
PubMed
Summary

This study presents an explicit solution for heat conduction in composite materials, offering a new method for analyzing heat flow across material interfaces without needing specific temperature or flux values.

Keywords:
Fokas methodcomposite wallsheat equationinterface problemnon-steady-state heat conduction

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Area of Science:

  • Physics
  • Materials Science
  • Applied Mathematics

Background:

  • Heat conduction in composite materials is crucial for many engineering applications.
  • Existing models often require specific boundary conditions at interfaces, which can be difficult to determine.
  • One-dimensional heat equation analysis is fundamental but complex for piecewise homogeneous materials.

Purpose of the Study:

  • To develop an explicit solution for the one-dimensional heat equation in piecewise homogeneous composite materials.
  • To analyze heat conduction where only continuity of temperature and heat flux at interfaces is assumed.
  • To provide a method applicable to various composite structures, including semi-infinite and finite domains.

Main Methods:

  • Solving the one-dimensional heat equation explicitly within each homogeneous domain.
  • Applying interface conditions based on the continuity of temperature and heat flux.
  • Developing analytical solutions for configurations of two semi-infinite domains and two finite-sized domains.

Main Results:

  • An explicit analytical solution for heat conduction in one-dimensional piecewise homogeneous materials is derived.
  • The method successfully handles interfaces where temperature and heat flux are not explicitly prescribed.
  • The solution framework is demonstrated for two semi-infinite and two finite-sized domains, with extensions outlined.

Conclusions:

  • The presented method offers a robust way to solve heat conduction problems in complex composite materials.
  • This approach simplifies analysis by relying on physical continuity principles at interfaces.
  • The solution is adaptable to more intricate composite structures, enhancing its practical utility.