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Journal of Central South University

, Volume 26, Issue 8, pp 2100–2108 | Cite as

Resolving double-sided inverse heat conduction problem using calibration integral equation method

  • Hong-chu Chen (陈鸿初)Email author
Article Heat and mass transfer
  • 11 Downloads

Abstract

In this paper, a novel calibration integral equation is derived for resolving double-sided, two-probe inverse heat conduction problem of surface heat flux estimation. In contrast to the conventional inverse heat conduction techniques, this calibration approach does not require explicit input of the probe locations, thermophysical properties of the host material and temperature sensor parameters related to thermal contact resistance, sensor capacitance and conductive lead losses. All those parameters and properties are inherently contained in the calibration framework in terms of Volterra integral equation of the first kind. The Laplace transform technique is applied and the frequency domain manipulations of the heat equation are performed for deriving the calibration integral equation. Due to the ill-posed nature, regularization is required for the inverse heat conduction problem, a future-time method or singular value decomposition (SVD) can be used for stabilizing the ill-posed Volterra integral equation of the first kind.

Key words

inverse heat conduction problem surface heat flux estimation calibration integral equation method 

用基于校准积分方程的方法解决双面导热反问题

摘要

本文推导了用双面双传感器导热反问题估计固体表面热流密度的校准积分方程。跟传统的用于 解决导热反问题的方法相比, 基于校准的方法不需要给定温度传感器的位置、材料的热物性参数以及 温度传感器的接触热阻、比热容和接线的导热损失。所有的这些参数都已包含在最后推导出的第一类 Volterra 积分方程中。拉普拉斯变换以及频域内的数学处理被用于校准积分方程的推导过程中。由于 导热反问题在数学上是病态的, 所以所有的导热反问题都需要进行正规则化处理, 将来时间方法或者 奇异值分解方法可以被用于稳定病态的第一类Volterra 积分方程。

关键词

导热反问题 估计表面热流密度 校准积分方程 

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Copyright information

© Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical, Aerospace and Biomedical EngineeringUniversity of TennesseeKnoxvilleUSA

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