Thermal solutions for a plate with an arbitrary temperature transient on one surface and convection on the other: Direct and inverse formulations

Albert E. Segall, Craig C. Schoof, Daniel E. Yastishock

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Thick plates that are thermally loaded on one surface with convection on the other are often encountered in engineering practice. Given this wide utility and the limitations of most existing solutions to an adiabatic boundary condition, generalized direct thermal solutions were first derived for an arbitrary surface loading as modeled by a polynomial and its coefficients on the loaded surface with convection on the other. Once formulated, the temperature solutions were then used with elasticity relationships to determine the resulting thermal stresses. Additionally, the Inverse thermal problem was solved using a least-squares determination of the aforementioned polynomial coefficients based on the direct-solution and temperatures measured at the surface with convection. Previously published relationships for a thick-walled cylinder with internal heating/cooling and external convection are also included for comparison. Given the versatility of the polynomial solutions advocated, the method appears well suited for complicated thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties do not vary with temperature.

Original languageEnglish (US)
Title of host publicationDesign and Analysis
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791858943
DOIs
StatePublished - Jan 1 2019
EventASME 2019 Pressure Vessels and Piping Conference, PVP 2019 - San Antonio, United States
Duration: Jul 14 2019Jul 19 2019

Publication series

NameAmerican Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP
Volume3
ISSN (Print)0277-027X

Conference

ConferenceASME 2019 Pressure Vessels and Piping Conference, PVP 2019
CountryUnited States
CitySan Antonio
Period7/14/197/19/19

Fingerprint

Polynomials
Temperature
Heat problems
Thermal stress
Elasticity
Thermodynamic properties
Hot Temperature
Convection
Boundary conditions
Cooling
Heating

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

Segall, A. E., Schoof, C. C., & Yastishock, D. E. (2019). Thermal solutions for a plate with an arbitrary temperature transient on one surface and convection on the other: Direct and inverse formulations. In Design and Analysis (American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP; Vol. 3). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/PVP2019-93313
Segall, Albert E. ; Schoof, Craig C. ; Yastishock, Daniel E. / Thermal solutions for a plate with an arbitrary temperature transient on one surface and convection on the other : Direct and inverse formulations. Design and Analysis. American Society of Mechanical Engineers (ASME), 2019. (American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP).
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Segall, AE, Schoof, CC & Yastishock, DE 2019, Thermal solutions for a plate with an arbitrary temperature transient on one surface and convection on the other: Direct and inverse formulations. in Design and Analysis. American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP, vol. 3, American Society of Mechanical Engineers (ASME), ASME 2019 Pressure Vessels and Piping Conference, PVP 2019, San Antonio, United States, 7/14/19. https://doi.org/10.1115/PVP2019-93313

Thermal solutions for a plate with an arbitrary temperature transient on one surface and convection on the other : Direct and inverse formulations. / Segall, Albert E.; Schoof, Craig C.; Yastishock, Daniel E.

Design and Analysis. American Society of Mechanical Engineers (ASME), 2019. (American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP; Vol. 3).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Segall AE, Schoof CC, Yastishock DE. Thermal solutions for a plate with an arbitrary temperature transient on one surface and convection on the other: Direct and inverse formulations. In Design and Analysis. American Society of Mechanical Engineers (ASME). 2019. (American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP). https://doi.org/10.1115/PVP2019-93313