The Influences of the Hyperbolic Two-Temperatures Theory on Waves Propagation in a Semiconductor Material Containing Spherical Cavity

Abstract

This article focuses on the study of redial displacement, the carrier density, the conductive and thermodynamic temperatures and the stresses in a semiconductor medium with a spherical hole. This study deals with photo-thermoelastic interactions in a semiconductor material containing a spherical cavity. The new hyperbolic theory of two temperatures with one-time delay is used. The internal surface of the cavity is constrained and the density of carriers is photogenerated by a heat flux at the exponentially decreasing pulse boundaries. The analytical solutions by the eigenvalues approach under the Laplace transformation approaches are used to obtain the solution of the problem and the inversion of the Laplace transformations is performed numerically. Numerical results for semiconductor materials are presented graphically and discussed to show the variations of physical quantities under the present model.

Energy ratio response at the interface of elastic and dual-porous thermoelastic half-spaces

“…Youssef and Bary [7] solved the perplexing problem surrounding the infinitely rapid thermal wave propagation inherent in the classical two-temperature theory. Using hyperbolic twotemperature theory, Bassiouny and Rajagopalan [8], Bassioouny [9], and Hobiny et al [10] conducted an investigation into various thermoelastic models. Wang and Li [11] introduced the term memory-dependent derivative (MDD), which involves transforming the fractional derivative (specifically, Caputo type [12]) into its integral form.…”

Photo-thermo-piezo-elastic waves in semiconductor medium subject to distinct two temperature models with higher order memory dependencies

“…Furthermore, addressing the paradoxical phenomenon of thermal wave propagation occurring at an infinite speed, Youssef and El-Bary (2018) introduced a new model called the hyperbolic-two-temperature (HTT), which pertains to the phenomenon of accelerating conductive and thermal temperatures. Hobiny et al (2022) conducted a comprehensive exploration of various thermoelastic models, analyzing their characteristics and behavior under the HTT framework. The investigation of heat equations that incorporate higher order time derivatives has been a recent area of focus for Abouelregal (2020aAbouelregal ( , 2020bAbouelregal ( , 2021aAbouelregal ( , 2021b, as evidenced by their publications.…”

“…Furthermore, addressing the paradoxical phenomenon of thermal wave propagation occurring at an infinite speed, Youssef and El-Bary (2018) introduced a new model called the hyperbolic-two-temperature (HTT), which pertains to the phenomenon of accelerating conductive and thermal temperatures. Hobiny et al (2022) conducted a comprehensive exploration of various thermoelastic models, analyzing their characteristics and behavior under the HTT framework.…”

Energy analysis at the interface of piezo/thermoelastic half spaces

“…Further, considering the accelerating thermal and conductive temperatures, Youssef and Bary (Youssef and El-Bary, 2018) discovered the new hyperbolic-two-temperature (HTT) model updated the CTT model and found a way to address the paradox of thermal wave propagation at infinite speed. Bassiouny and Rajagopalan (2020), Bassiouny (2021) and Hobiny et al (2022) investigated the different thermoelastic models in the framework of the HTT theory. Wang and Li (2011) introduced a new concept of memory-dependent derivative (MDD), in which the first order of function f, for delay time t > 0, the kernel function k (t À z) can be chosen arbitrarily on a slipping interval [(t Àt),t] simply defined in integral form as follows:…”

“…Further, considering the accelerating thermal and conductive temperatures, Youssef and Bary (Youssef and El-Bary, 2018) discovered the new hyperbolic-two-temperature (HTT) model updated the CTT model and found a way to address the paradox of thermal wave propagation at infinite speed. Bassiouny and Rajagopalan (2020), Bassiouny (2021) and Hobiny et al (2022) investigated the different thermoelastic models in the framework of the HTT theory.…”