Analytical solution of fractional order heat equation under the effects of variable thermal conductivity during photothermal excitation of spherical cavity of semiconductor medium

Abstract: The influence of hydrostatic initial stress in the context of the time-fractional heat order equation is investigated The strong electromagnetic field is applied at the external surface of semiconductor elastic medium during the photothermal transport process The Thomson influence appears due to the strong magnetic field The behavior of wave propagations of the elastic medium is obtained in context of the thermoelectricity theory with initial stress The governing main equations are taken in two dimensions to describe the interaction between elastic-thermal-plasma and electromagnetic waves for fractional cases The density of charge is studied as a function of time only when the electric current is induced The separation of variables is used as a mathematical technique to obtain the exact solutions of the distributions of physical quantities under investigation Some mechanical, thermal, plasma and magnetic conditions are applied at the free surface elastic medium A numerical simulation is used to obtain physical quantities distributions graphically and discussed theoretically in various fractional cases

Abstract: The present study is concerned with the reflection and propagation of thermoelastic harmonic plane waves from the stress-free and isothermal surface of a homogeneous, isotropic thermally conducting elastic half-space in the frame of the modified Green–Lindasy (MGL) theory of generalized thermoelasticity with strain rate proposed by Yu et al (Meccanica 53:2543–2554, 2018) The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation Different from the thermoelastic coupling effect, there also exists one independent vertically shear-type (SV-type) wave In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV-type wave is not only dispersive in nature but also experiences attenuation Analytical expressions for the amplitude ratios of the reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface The paper concludes with the numerical results on the phase speeds and the amplitude ratios for specific parameter choices Various graphs have been plotted to analyze the behavior of these quantities The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the GL and LS models

Abstract: In the present paper, we constructed a new mathematical model of a thermoelastic semiconducting solid sphere based on the L-S model to study the photothermal interaction. Among this work, we considered the fractional-order strain, which has been introduced by Youssef. The bounding surface of the sphere has been thermally loaded by a thermal shock. Laplace transform has been applied, and its inversions have been obtained numerically. For silicon (Si) material, the numerical results of the temperature increment, carrier density increment, strain, displacement, stress, and stress-strain energy have been represented in figures with various values of the fractional-order parameter, relaxation time parameter, and reference temperature. The relaxation time parameter and reference temperature have significant effects on all the studied functions. The fractional-order parameter has limited effects on the temperature increment and carrier density increment, while it has significant effects on the strain, displacement, stress, and stress-strain energy.

Abstract: This paper is dealing with the photothermal interaction of a homogenous, isotropic, semiconducting, viscothermoelastic solid cylinder in the context of Green-Naghdi theories of generalized thermoelasticity (type-I, -II, and -III). The ramp-type heating has thermally loaded the bounding surface of the cylinder. The governing equations have been constructed in the Laplace transform domain, and the Laplace inversions have been calculated numerically by using the Tzou method. The numerical results for the carrier density increment, temperatures increment, strain, stress, and stress-strain energy have been represented in figures with various values of mechanical relaxation time and ramp-time heat parameter. The mechanical relaxation time has minimal effects on the carrier density function and temperature increment, while its effects on the strain, stresses, and stress-strain energy are significant. The ramp-time heat parameter has significant effects on all the studied functions.

Abstract: The present paper is dealing with a new mathematical model of a thermoelastic semiconducting solid sphere based on the Green-Naghdi theories to study the photothermal interaction. We applied two co...

Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.

Abstract: A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.

Abstract: This paper reviews the theory and applications of photoacoustic (also called optoacoustic) methods belonging to the more general area of photothermal measurement techniques. The theory covers excitation of gaseous or condensed samples with modulated continuous light beams or pulsed light beams. The applications of photoacoustic methods include spectroscopy, monitoring deexcitation processes, probing physical properties of materials, and generating mechanical motions. Several other related photothermal methods, as well as particle-acoustics and wave-acoustics methods are also described. This review complements an earlier and narrower review [Rev. Mod. Phys. 53, 517 (1981)] that is mainly concerned with sensitive detection by pulsed photoacoustic spectroscopy in condensed matter.

Abstract: In this paper a numerical inversion method for Laplace transforms, based on a Fourier series expansion developed by Durbin [5], is presented. The disadvantage of the inversion methods of that type, the encountered dependence of discretization and truncation error on the free parameters, is removed by the simultaneous application of a procedure for the reduction of the discretization error, a method for accelerating the convergence of the Fourier series and a procedure that computes approximately the ‘best’ choice of the free parameters. Suitable for a given problem, the inversion method allows the adequate application of these procedures. Therefore, in a big range of applications a high accuracy can be achieved with only a few function evaluations of the Laplace transform. The inversion method is implemented as a FORTRAN subroutine.

Abstract: Buildup and decay transients were observed when polar or nonpolar liquid cells were placed within the resonator of a helium—neon laser operating in the red at 6328 A. Similar but smaller effects were also observed with two solids. Time constants were the order of a few seconds for all materials, which suggests a thermal phenomenon, but general heating effects were ruled out by the strong localization of the phenomenon. Transverse motion of the cell by about one beam width caused new transients similar to the initial ones.It is believed that the effects are caused by absorption of the red light in the material, producing a local heating in the vicinity of the beam and a lens effect arising from the transverse gradient of refractive index. Absorptions of 10−3 to 10−4 parts per centimeter are sufficient to produce the effects, and are believed to be reasonable values for the materials studied. One of the most important applications may in fact be for the measurement of small absorbancies.The experiments are ...