### Abstract

The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

Original language | English |
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Pages (from-to) | 2468-2475 |

Number of pages | 8 |

Journal | Journal of Physics D: Applied Physics |

Volume | 38 |

Issue number | 14 |

DOIs | |

Publication status | Published - 2005 Jul 21 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Acoustics and Ultrasonics
- Surfaces, Coatings and Films

### Cite this

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**Electrothermal crack analysis in a finite conductive layer with temperature-dependent material properties.** / Jang, Yong Hoon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Electrothermal crack analysis in a finite conductive layer with temperature-dependent material properties

AU - Jang, Yong Hoon

PY - 2005/7/21

Y1 - 2005/7/21

N2 - The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

AB - The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

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UR - http://www.scopus.com/inward/citedby.url?scp=22144498873&partnerID=8YFLogxK

U2 - 10.1088/0022-3727/38/14/025

DO - 10.1088/0022-3727/38/14/025

M3 - Article

AN - SCOPUS:22144498873

VL - 38

SP - 2468

EP - 2475

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 14

ER -