Multiple scattering of thermal waves from double subsurface cylinders in semi‐infinite slab

Abstract

In this paper, combined with the non-Fourier equation of heat conduction and expansion method of wave functions, the multiple scattering of thermal waves from a subsurface cylinder in a semi-infinite body is investigated. A general solution of scattered fields based on hyperbolic equations of heat conduction is presented for the first time. The effects of physical and geometric parameters on the temperature are analyzed. The thermal waves are excited at the front surface of opaque material by modulated optical beams. The circular cylinder is taken as a cavity with thermal insulation conditions.

Scattering of thermal waves by a heterogeneous subsurface spheroid inclusion including non-Fourier effects

“…The spheroid inclusion is assumed one with adiabatic condition (l 0 /l = 0), and the temperature distribution on the frontal surface is consistent with the results from Refs. [10,17]; therefore, the method proposed in this paper would be considered as correct. In the following section, the method is used to analyse thermal wave scattering and the temperature distribution on the frontal surface of solids containing subsurface defects with thermal boundary conditions of the adiabatic.…”

“…ð2n þ 1Þi n j n ðkrÞP n ðcosuÞexpðÀivtÞ (10) where # 0 are the amplitudes of the incident thermal waves, j n ðÁÞ is the nth spherical Bessel function of the first kind, and P n ðxÞ ¼ P 0 n ðxÞ are the Legendre functions.…”

“…The sample surface is heated by an extended light beam modulated at a frequency f that produces planar thermal waves. The thermal waves can be described using the following hyperbolic equation of heat conduction, which is based on nonFourier heat conduction [10]:…”

“…Regular geometries, such as planes, spheres, and cylinders, can be analysed with a high degree of accuracy and have been investigated in detail by several groups [6][7][8][9][10][11]. These studies are mainly based on Fourier's law of heat conduction.…”

“…These studies are mainly based on Fourier's law of heat conduction. Fourier's law requires an assumption that the propagation speed of a thermal disturbance in a medium is infinite; therefore, it is unsuitable for the study of micro-scale heat transfers [10]. When the surfaces of opaque materials are heated by modulated, ultra-short laser pulses, the heat propagation in the materials have wave characteristics [12], and non-Fourier effects should be taken into account.…”