Effect of gravity on generalized thermoelastic diffusion due to laser pulse using dual-phase-lag model

Abstract

Purpose The purpose of this paper is to obtain a general solution to the field equations of generalized thermo-diffusion in an infinite thermoelastic body under the effect of gravity in the context of the dual-phase-lag (DPL) model. The half space is considered made of an isotropic homogeneous thermoelastic material. The boundary plane surface is heated by a non-Gaussian laser beam. Design/methodology/approach An exact solution to the problem is obtained using the normal mode analysis. Findings The derived expressions are computed numerically for copper and the results are presented in graphical form. Originality/value Comparisons are made with the results predicted by Lord-Shulman theory and DPL model for different values of time and in the presence and absence of gravity as well as diffusion.

A laser pulse impactful on a half-space using the modified TPL G–N models

“…It is to be noted that Eqs. (6) and 7represent two forms of the simple G-N II model, the first is in terms of the rate of thermal conductivity k * while the second is in terms of the heat conductivity coefficient k. A lot of investigators have dealt with the simple G-N II and III models while other investigators have dealt with the TPL G-N III model (N = 1) [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] . All these models are presented without the higher-order time derivatives as those presented in this study.…”

State-space approach to nonlocal thermo-viscoelastic piezoelectric materials with fractional dual-phase lag heat transfer

“…0, the DPL model simplifies to Fourier's law, a technique in which a temperature gradient is produced throughout a material volume over time t þ t u will not give rise to a thermal flux at a point x within that volume until the later time t þ t q . Refer to El-Karamany and Ezzat (2013Ezzat ( , 2014; Othman and Abd-Elaziz (2017), Othman and Eraki (2018); Othman et al (2019); and Aldawody et al (2019) for further information on the DPL model. Tzou and Guo (2010) has expanded their DPL model by incorporating the nonlocal length, which is depicted as:…”

A thermoelastic micro‐elongated layer under the effect of gravity in the context of the dual‐phase lag model

“…A new model called the dual‐phase‐lag model for a heat transport mechanism in which an approximation replaces Fourier's law to a modification of Fourier's law with two different time translations for the heat flux and the temperature gradient was developed by Tzou [5,6]. The effect of gravity on generalized thermoelastic diffusion due to laser pulse utilizing the (DPL) model was introduced by Othman and Eraki [7]. The theory that material particles in solids can undergo macro‐deformations and micro‐rotations was proposed by Eringen [8–10] and referred to as the “linear theory of micro‐polar elasticity.” Later, Eringen [11] also developed the theory of thermo‐microstretch elastic solids.…”