### Abstract

A common threat to thick-walled vessels and pipes is thermal shock from operational steady-state or transient thermoelastic stresses. As such, boundary conditions must be known or determined in order to reveal the underlying thermal state. For direct problems where all boundary conditions are known, the procedure is relatively straightforward and mathematically tractable as shown by recent studies. Although more practical from a measurement standpoint, the inverse problem where boundary conditions must be determined from remotely determined temperature and/or flux data is ill-posed and inherently sensitive to errors in the data. As a result, the inverse route is rarely used to determine thermal-stresses. Moreover, most analytical solutions to the inverse problem rely on a host of assumptions that usually restrict their utility to timeframes before the thermal wave reaches the natural boundaries of the structure. To help offset these limitations and at the same, time solve for the useful case of a thick-walled cylinder exposed to thermal loading on the ID, the inverse problem was solved using a least-squares determination of polynomial coefficients based on a generalized direct-solution to the Heat Equation. Once the inverse problem was solved in this fashion and the unknown boundary-condition on the ID determined, the resulting polynomial was used with the generalized direct solution to estimate the internal temperature and stress distributions as a function of time and radial position. For a thick-walled cylinder under an internal transient with external convection, excellent agreement was seen with various measured temperature histories. Given the versatility of the polynomial solutions advocated, the method appears well suited for many thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature.

Original language | English (US) |
---|---|

Article number | PVP2005-71054 |

Pages (from-to) | 487-493 |

Number of pages | 7 |

Journal | American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP |

Volume | 3 |

DOIs | |

State | Published - Dec 22 2005 |

Event | 2005 ASME Pressure Vessels and Piping Conference, PVP2005 - Denver, CO, United States Duration: Jul 17 2005 → Jul 21 2005 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mechanical Engineering

### Cite this

}

**Thermoelastic stresses in thick-walled vessels under an arbitrary thermal transient via the inverse route.** / Segall, Albert Eliot.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Thermoelastic stresses in thick-walled vessels under an arbitrary thermal transient via the inverse route

AU - Segall, Albert Eliot

PY - 2005/12/22

Y1 - 2005/12/22

N2 - A common threat to thick-walled vessels and pipes is thermal shock from operational steady-state or transient thermoelastic stresses. As such, boundary conditions must be known or determined in order to reveal the underlying thermal state. For direct problems where all boundary conditions are known, the procedure is relatively straightforward and mathematically tractable as shown by recent studies. Although more practical from a measurement standpoint, the inverse problem where boundary conditions must be determined from remotely determined temperature and/or flux data is ill-posed and inherently sensitive to errors in the data. As a result, the inverse route is rarely used to determine thermal-stresses. Moreover, most analytical solutions to the inverse problem rely on a host of assumptions that usually restrict their utility to timeframes before the thermal wave reaches the natural boundaries of the structure. To help offset these limitations and at the same, time solve for the useful case of a thick-walled cylinder exposed to thermal loading on the ID, the inverse problem was solved using a least-squares determination of polynomial coefficients based on a generalized direct-solution to the Heat Equation. Once the inverse problem was solved in this fashion and the unknown boundary-condition on the ID determined, the resulting polynomial was used with the generalized direct solution to estimate the internal temperature and stress distributions as a function of time and radial position. For a thick-walled cylinder under an internal transient with external convection, excellent agreement was seen with various measured temperature histories. Given the versatility of the polynomial solutions advocated, the method appears well suited for many thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature.

AB - A common threat to thick-walled vessels and pipes is thermal shock from operational steady-state or transient thermoelastic stresses. As such, boundary conditions must be known or determined in order to reveal the underlying thermal state. For direct problems where all boundary conditions are known, the procedure is relatively straightforward and mathematically tractable as shown by recent studies. Although more practical from a measurement standpoint, the inverse problem where boundary conditions must be determined from remotely determined temperature and/or flux data is ill-posed and inherently sensitive to errors in the data. As a result, the inverse route is rarely used to determine thermal-stresses. Moreover, most analytical solutions to the inverse problem rely on a host of assumptions that usually restrict their utility to timeframes before the thermal wave reaches the natural boundaries of the structure. To help offset these limitations and at the same, time solve for the useful case of a thick-walled cylinder exposed to thermal loading on the ID, the inverse problem was solved using a least-squares determination of polynomial coefficients based on a generalized direct-solution to the Heat Equation. Once the inverse problem was solved in this fashion and the unknown boundary-condition on the ID determined, the resulting polynomial was used with the generalized direct solution to estimate the internal temperature and stress distributions as a function of time and radial position. For a thick-walled cylinder under an internal transient with external convection, excellent agreement was seen with various measured temperature histories. Given the versatility of the polynomial solutions advocated, the method appears well suited for many thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature.

UR - http://www.scopus.com/inward/record.url?scp=29144509696&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29144509696&partnerID=8YFLogxK

U2 - 10.1115/PVP2005-71054

DO - 10.1115/PVP2005-71054

M3 - Conference article

AN - SCOPUS:29144509696

VL - 3

SP - 487

EP - 493

JO - American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP

JF - American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP

SN - 0277-027X

M1 - PVP2005-71054

ER -