Abstract
With the application to engineering practice, the study of the scattering of thermal waves using innovative and comprehensive methods is becoming increasingly important. The thermal wave scattering by an elliptic subsurface hole in a block with two boundaries is discussed based on the non-Fourier heat conduction equation, employing the complex function method and the conformal mapping method, and a general solution for the thermal wave scattering is given. The numerical results of temperature distributions around a subsurface hole are presented and the effects of geometrical and physical parameters on the temperature distributions were analyzed. The wave number, the shape and position of the hole, the scale of the block, and the frequency of the heat load were found to have great effects on distributions and variations of temperature. The findings of this study could be helpful in providing better understandings of infrared thermal wave imaging, the physical inverse problem, and the evaluation of internal holes in materials.
Highlights
Subsurface defects can be detected and evaluated by tuning the temperature in the thermal wave field, since the frequency and amplitude of ultra-short laser pulses can be controlled [1,2,3]
It is an accessible way to get the subsurface micro-structure information and to realize thermal wave detection according to the real-time measurement of the temperature field on the solid surface
When the temperature increases quickly, the heat conduction process in solids should be described by a hyperbolic equation, which means that only wave equations can be used to illustrate the features and properties of the heat conduction process [4,5,6]
Summary
Subsurface defects can be detected and evaluated by tuning the temperature in the thermal wave field, since the frequency and amplitude of ultra-short laser pulses can be controlled [1,2,3]. Many researchers have attached much importance to the potential practical values of non-Fourier heat conduction in many applications, and non-Fourier heat conduction has become one of the hotspots in the field of heat transfer It can evaluate the applicable conditions for the classic heat conduction equation, which has great prospects in theory and engineering for analyzing the thermal wave multiple scattering and temperature distribution with the hyperbolic heat conduction equation. The shapes of scattered bodies are almost always assumed to be circular and the effects resulting from the finiteness of other scales in project practice are ignored [16,18] This means that the applications of the theories outlined above have limitations in engineering practice. The main objective of this paper was to investigate the multiple scattering of thermal waves by a subsurface, non-circular hole in an infinite block with two boundaries, based on the non-Fourier heat conduction hyperbolic equation. This paper brings about an important significance in solving the problem of the scattering of thermal waves by holes in any shapes [19]
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