### Abstract

Analytical solutions for one-dimensional time dependent multilayer heat conduction problems were developed several decades ago. Mathematical theory for such problems in more than one dimensions was also developed during that time. Several of these methods were based on separation of variable and finite integral transform. However, the application of these methods was hindered by the fact that the eigenvalue problems, which are essential for this methodology are difficult to solve. Moreover, in two and three dimensional Cartesian coordinates these eigenvalues were imaginary rendering their solutions even more difficult. It has been recently shown that similar problems in two dimensional cylindrical and spherical coordinates do not have imaginary eigenvalues. It is also helpful that the softwares which are capable of analytical manipulations are now ubiquitous. This paper discusses the methodology as well as possible application in nuclear reactors of analytical solutions of two-dimensional multilayer heat conduction in spherical and cylindrical coordinates.

Original language | English (US) |
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Title of host publication | 2010 1st International Nuclear and Renewable Energy Conference, INREC'10 |

DOIs | |

State | Published - 2010 |

Event | 2010 1st International Nuclear and Renewable Energy 2010 1st International Nuclear and Renewable Energy Conference, INREC'10 - Amman, Jordan |

### Other

Other | 2010 1st International Nuclear and Renewable Energy 2010 1st International Nuclear and Renewable Energy Conference, INREC'10 |
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Country | Jordan |

City | Amman |

Period | 3/21/10 → 3/24/10 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear Energy and Engineering
- Renewable Energy, Sustainability and the Environment

### Cite this

*2010 1st International Nuclear and Renewable Energy Conference, INREC'10*[5462601] DOI: 10.1109/INREC.2010.5462601

**Analytical solution of time-dependent multilayer heat conduction problems for nuclear applications.** / Singh, Suneet; Jain, Prashant K.; Rizwan-uddin.

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

*2010 1st International Nuclear and Renewable Energy Conference, INREC'10.*, 5462601, 2010 1st International Nuclear and Renewable Energy 2010 1st International Nuclear and Renewable Energy Conference, INREC'10, Amman, Jordan, 21-24 March. DOI: 10.1109/INREC.2010.5462601

}

TY - CHAP

T1 - Analytical solution of time-dependent multilayer heat conduction problems for nuclear applications

AU - Singh,Suneet

AU - Jain,Prashant K.

AU - Rizwan-uddin,

PY - 2010

Y1 - 2010

N2 - Analytical solutions for one-dimensional time dependent multilayer heat conduction problems were developed several decades ago. Mathematical theory for such problems in more than one dimensions was also developed during that time. Several of these methods were based on separation of variable and finite integral transform. However, the application of these methods was hindered by the fact that the eigenvalue problems, which are essential for this methodology are difficult to solve. Moreover, in two and three dimensional Cartesian coordinates these eigenvalues were imaginary rendering their solutions even more difficult. It has been recently shown that similar problems in two dimensional cylindrical and spherical coordinates do not have imaginary eigenvalues. It is also helpful that the softwares which are capable of analytical manipulations are now ubiquitous. This paper discusses the methodology as well as possible application in nuclear reactors of analytical solutions of two-dimensional multilayer heat conduction in spherical and cylindrical coordinates.

AB - Analytical solutions for one-dimensional time dependent multilayer heat conduction problems were developed several decades ago. Mathematical theory for such problems in more than one dimensions was also developed during that time. Several of these methods were based on separation of variable and finite integral transform. However, the application of these methods was hindered by the fact that the eigenvalue problems, which are essential for this methodology are difficult to solve. Moreover, in two and three dimensional Cartesian coordinates these eigenvalues were imaginary rendering their solutions even more difficult. It has been recently shown that similar problems in two dimensional cylindrical and spherical coordinates do not have imaginary eigenvalues. It is also helpful that the softwares which are capable of analytical manipulations are now ubiquitous. This paper discusses the methodology as well as possible application in nuclear reactors of analytical solutions of two-dimensional multilayer heat conduction in spherical and cylindrical coordinates.

UR - http://www.scopus.com/inward/record.url?scp=77953282661&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953282661&partnerID=8YFLogxK

U2 - 10.1109/INREC.2010.5462601

DO - 10.1109/INREC.2010.5462601

M3 - Conference contribution

SN - 9781424452149

BT - 2010 1st International Nuclear and Renewable Energy Conference, INREC'10

ER -