Applying the solotone inverse method to estimate thermophysical properties of bonds and to locate internal boundaries, including regions of porosity

Abstract

In previous work the author presented a novel method whereby relative values of the specific heat capacity and thermal conductivity of a composite rod may be accurately estimated by analyzing oscillations present within eigenvalue spectra. This work described how the solotone effect may be utilized to solve a parameter estimation inverse problem. In this paper, we show how the solotone inverse method may also be used to solve inverse geometry problems. Three different heat conduction inverse problems are considered. First, the method is used to estimate the thermophysical properties of a bond. Second, the solotone effect is used to locate a narrow porous region within an otherwise solid rod. Both of these examples pertain to the one-dimensional layered composite rod considered in previous work. Our third example concerns heat conduction in a composite layered hemisphere, and in this example the solotone inverse method is used to estimate the dimensions of an internal hemispherical layer. Examples two and three demonstrate the ability of the solotone inverse method to solve inverse geometry problems, thus extending the applicability of this method.

Keywords:

• Eigenvalue spectra
• solotone effect
• heat transfer
• inverse problems
• manufacturing technology

2010 Mathematics Subject Classification:

• 35P20

Acknowledgments

I would like to thank the anonymous reviewers for providing valuable suggestions during the development of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.