0
RESEARCH PAPERS

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

[+] Author and Article Information
A. E. Segall

Engineering Science and Mechanics, The Pennsylvania State University, 212 EES Building, University Park, PA 16803aesegall@psu.edu

J. Pressure Vessel Technol 128(4), 599-604 (Jan 19, 2006) (6 pages) doi:10.1115/1.2349573 History: Received July 24, 2005; Revised January 19, 2006

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Thick-walled geometry and know and unknown boundary conditions at the external and internal surfaces, respectively

Grahic Jump Location
Figure 2

Comparison of inverse predictions and asymptotic thermal loading of an infinitely long and hollow cylinder as a function of nondimensional time (a∕b=0.667 and Bi=12)

Grahic Jump Location
Figure 3

Comparison of transient temperature distribution across the radius of a cylinder subjected to an exponential heating on the internal surface with convection on the outer surface (a∕b=0.667 and Bi=12)

Grahic Jump Location
Figure 4

Comparison of inverse predictions and triangular thermal-loading of an infinitely long and hollow cylinder as a function of nondimensional time (a∕b=0.667 and Bi=12)

Grahic Jump Location
Figure 5

Comparison of transient hoop-stress distributions across the radius of a cylinder subjected to exponential heating on the internal surface and convection on the outer surface (a∕b=0.667 and Bi=12)

Grahic Jump Location
Figure 6

Comparison of the transient axial-stress distributions across the radius of a cylinder subjected to exponential heating on the internal surface and convection on the outer surface (a∕b=0.667 and Bi=12)

Grahic Jump Location
Figure 7

Comparison of transient radial stress distributions across the radius of a cylinder subjected to exponential heating on the internal surface and convection on the outer surface (a∕b=0.667 and Bi=12)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In