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 (temperature or flux) are known, the procedure is relatively straightforward and mathematically tractable as shown by many studies. Although more practical from a measurement standpoint, the inverse problem where the 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 time frames 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 internal surface, 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 internal surface determined, the resulting polynomial was used with the generalized direct solution to determine 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 known 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.

Skip Nav Destination

aesegall@psu.edu

Article navigation

November 2006

Research Papers

# Thermoelastic Stresses in Thick-Walled Vessels Under Thermal Transients via the Inverse Route

A. E. Segall

A. E. Segall

Member ASME

Engineering Science and Mechanics,

aesegall@psu.edu
The Pennsylvania State University

, 212 EES Building, University Park, PA 16803
Search for other works by this author on:

A. E. Segall

Member ASME

Engineering Science and Mechanics,

The Pennsylvania State University

, 212 EES Building, University Park, PA 16803aesegall@psu.edu

*J. Pressure Vessel Technol*. Nov 2006, 128(4): 599-604 (6 pages)

**Published Online:**January 19, 2006

Article history

Received:

July 24, 2005

Revised:

January 19, 2006

Citation

Segall, A. E. (January 19, 2006). "Thermoelastic Stresses in Thick-Walled Vessels Under Thermal Transients via the Inverse Route." ASME. *J. Pressure Vessel Technol*. November 2006; 128(4): 599–604. https://doi.org/10.1115/1.2349573

Download citation file:

### Get Email Alerts

### Cited By

Investigation in the Natural Frequency of Wound Tube for Coil-Wound Heat Exchanger

J. Pressure Vessel Technol

Theoretical Study On Thermal Hydraulic Expansion Process of Stainless Steel Lined Clad Pipe

J. Pressure Vessel Technol

### Related Articles

Approximate Direct and Inverse Relationships for Thermal and Stress States in Thick-Walled Vessels Under Thermal Shock

J. Pressure Vessel Technol (February,2007)

Transient Surface Strains and the Deconvolution of Thermoelastic States and Boundary Conditions

J. Pressure Vessel Technol (February,2009)

Thermal Stresses in an Infinite Slab Under an Arbitrary Thermal Shock

J. Appl. Mech (September,2003)

Thermoelastic Stresses in an Axisymmetric Thick-Walled Tube Under an Arbitrary Internal Transient

J. Pressure Vessel Technol (August,2004)

### Related Chapters

Analysis of Components in VIII-2

Guidebook for the Design of ASME Section VIII Pressure Vessels, Third Edition

Flexibility Analysis

Process Piping: The Complete Guide to ASME B31.3, Third Edition

Interface with Stationary Equipment

Pipe Stress Engineering