### Abstract

In this paper steady heat conduction in Cartesian coordinates is discussed with the method of Green's functions for the slab, the rectangle, and the parallelepiped. The commonality among the components of the GF for 1-D, 2-D, and 3-D bodies is emphasized. The relationship between higher-dimension Green's functions and the lower-dimension Green's functions is discussed. There are at least two and sometimes several alternative expressions for each Green's function, and the alternative Green's functions are very important for construction of rapidly-converging series useful for numerical evaluation. A Green's Functions Library is described in which the Green's functions are organized according to a unique numbering system and are available on the world-wide web (http://www.engr.unl.edu/~glibrary/).

Original language | English (US) |
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Title of host publication | Proceedings of the 2001 National Heat Transfer Conference Volume 2 |

Pages | 1373-1382 |

Number of pages | 10 |

State | Published - Dec 1 2001 |

Event | 2001 National Heat Transfer Conference (NHTC2001) - Ananheim, CA, United States Duration: Jun 10 2001 → Jun 12 2001 |

### Publication series

Name | Proceedings of the National Heat Transfer Conference |
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Volume | 2 |

### Conference

Conference | 2001 National Heat Transfer Conference (NHTC2001) |
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Country | United States |

City | Ananheim, CA |

Period | 6/10/01 → 6/12/01 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Engineering (miscellaneous)

### Cite this

*Proceedings of the 2001 National Heat Transfer Conference Volume 2*(pp. 1373-1382). (Proceedings of the National Heat Transfer Conference; Vol. 2).

**Steady heat conduction in Cartesian coordinates and a library of Green's functions.** / Cole, Kevin D; Crittenden, Paul E.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2001 National Heat Transfer Conference Volume 2.*Proceedings of the National Heat Transfer Conference, vol. 2, pp. 1373-1382, 2001 National Heat Transfer Conference (NHTC2001), Ananheim, CA, United States, 6/10/01.

}

TY - GEN

T1 - Steady heat conduction in Cartesian coordinates and a library of Green's functions

AU - Cole, Kevin D

AU - Crittenden, Paul E.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - In this paper steady heat conduction in Cartesian coordinates is discussed with the method of Green's functions for the slab, the rectangle, and the parallelepiped. The commonality among the components of the GF for 1-D, 2-D, and 3-D bodies is emphasized. The relationship between higher-dimension Green's functions and the lower-dimension Green's functions is discussed. There are at least two and sometimes several alternative expressions for each Green's function, and the alternative Green's functions are very important for construction of rapidly-converging series useful for numerical evaluation. A Green's Functions Library is described in which the Green's functions are organized according to a unique numbering system and are available on the world-wide web (http://www.engr.unl.edu/~glibrary/).

AB - In this paper steady heat conduction in Cartesian coordinates is discussed with the method of Green's functions for the slab, the rectangle, and the parallelepiped. The commonality among the components of the GF for 1-D, 2-D, and 3-D bodies is emphasized. The relationship between higher-dimension Green's functions and the lower-dimension Green's functions is discussed. There are at least two and sometimes several alternative expressions for each Green's function, and the alternative Green's functions are very important for construction of rapidly-converging series useful for numerical evaluation. A Green's Functions Library is described in which the Green's functions are organized according to a unique numbering system and are available on the world-wide web (http://www.engr.unl.edu/~glibrary/).

UR - http://www.scopus.com/inward/record.url?scp=0346275129&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346275129&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0791835332

SN - 9780791835333

T3 - Proceedings of the National Heat Transfer Conference

SP - 1373

EP - 1382

BT - Proceedings of the 2001 National Heat Transfer Conference Volume 2

ER -