Photo-Thermal Interactions in a Semiconducting Media with a Spherical Cavity under Hyperbolic Two-Temperature Model

Faris S Alzahrani,Ibrahim A Abbas

doi:10.3390/math8040585

Abstract

This article highlights the study of photo-thermoelastic interaction in an unbounded semiconductor medium containing a spherical cavity. This problem is solved using the new hyperbolic two-temperature model. The bounding surface of the cavity is traction free and loaded thermally by exponentially decaying pulse boundary heat flux. In addition, the carrier density is prescribed on the inner surface of the cavity in terms of the recombination speed. The techniques of Laplace transforms are used to get the analytical solutions of the problem in the transformed domain by the eigenvalues method. The inversions of Laplace transformations have been carried out numerically. The outcomes also display that the analytical schemes can overcome the mathematical problem to analyze this problem. Numerical outcomes for a semiconductor material are performed and demonstrated graphically. According to the numerical results, this new hyperbolic two-temperature model of thermoelasticity offers finite speed of the thermal wave and mechanical wave propagation.

Highlights

The thermoelasticity model with the classical two-temperature model is presented by Williams and Gurtin [1], Chen and Gurtin [2] and Chen et al [3]; when using another temperature depending on the classic two temperatures, the classical inequality of Clausius-Duhem has been substituted
Ezzat et al [4] investigated the effects of fractional order and two-temperature theory in magneto-thermoelasticity under dual-phase-lag heat transfer
The conditions on the inner surface of the cavity are due to heat flux with an exponentially decaying pulse [29]

Summary

Introduction

The thermoelasticity model with the classical two-temperature model is presented by Williams and Gurtin [1], Chen and Gurtin [2] and Chen et al [3]; when using another temperature depending on the classic two temperatures (thermodynamic temperature T∗ and conductivity temperature φ∗ ), the classical inequality of Clausius-Duhem has been substituted. This paper describes investigations that try to measure the transport process based on the principles of optical beams deviation through a photothermal technique that can be considered as an expansion of the photothermal deviation approach These techniques are characterized as having no contact and directly producing the parameters of electronics and heat transport on the surface of the semiconductor or at the interface and within most of the semiconducting material. Yasein et al [14] studied the influence of variable thermal conductivity of one-dimensional semiconducting media under photothermal excitations due to ramp type heating. Et al [14] studied the influence of variable thermal conductivity of a semiconductor elastic medium during photothermal excitation subjected to thermal ramp type. The outcomes are illustrated graphically to show the differences among the hyperbolic two-temperature model, the classical two-temperature model, and the one temperature model

Formulation of the Problem

Initial and Boundary Conditions

Method of Solution

Numerical Results and Discussions

Conclusions