Prof. Dr. Ibrahim A. Abbas

Professor - Department of Mathematics

Faculty of science

Address: Sohag University, Egypt.


A DPL model of photo-thermal interaction in an infinite semiconductor material containing a spherical hole
The dual phase lag (DPL) heat transfer model is applied to study the photo-thermal interaction in an infinite semiconductor medium containing a spherical hole. The inner surface of the cavity was traction free and loaded thermally by pulse heat flux. By using the eigenvalue approach methodology and Laplace’s transform, the physical variable solutions are obtained analytically. The numerical computations for ... Read more

Photo-thermal-elastic interaction in an unbounded semiconducting medium with spherical cavity due to pulse heat flux
In this work, the photothermal waves in an unbounded semiconducting medium with spherical cavity are studied. This problem is solved using the theory of coupled plasma, thermal, and elastic wave. An unbounded material, elastic semiconductor containing a spherical cavity with isotropic and homogeneous thermal and elastic properties has been considered. The inner surface of the cavity is taken traction-free and ... Read more

Fractional order photo-thermo-elastic waves in a two-dimensional semiconductor plate
This paper is devoted to the investigation of fractional order photo-thermo-elastic waves in a two-dimensional semiconductor using the eigenvalues approach. The formulations applied are based on the fractional order generalized thermo-elasticity in the context of the new model of heat conduction. The bounding surface of the plate is taken to be stress-free and exposed to a heat flux with the ... Read more

Finite Element Analysis of Thermoelastic Fiber-Reinforced Anisotropic Hollow Cylinder with Dual-Phase-Lag Model
In the present paper, we have constructed the equations for generalized thermoelasticity of a fiber-reinforced anisotropic hollow cylinder. The formulation is applied in the context of dualphase-lag model. An application of hollow cylinder is investigated for the outer surface is traction free and thermally isolated, while the inner surface is traction free and subjected to thermal shock. The problem is ... Read more

A Green-Naghdi Model in a 2D Problem of a Mode I Crack in an Isotropic Thermoelastic Plate
In this article, the generalized thermoelastic theory under Green and Naghdi models are used to study the thermoelastic interaction in an isotropic material containing a finite crack inside the material. The crack boundary is due to a prescribed temperature and stress distribution. Based on the Green-Naghdi type II and type III models, the formulation is applied to generalized thermoelasticity with ... Read more

Free Vibrations of Nanoscale Beam Under Two-Temperature Green and Naghdi Model
The influence of the coupling between strain rate and temperature becomes domineering in the nanoscale beam. In this work, the free vibration of nanoscale beam resonators is analysed using Green and Naghdi's theorem under the two-temperature model (2TGNIII). The influence of two-temperature parameters in a nanoscale beam is studied for beams under simply supported conditions. Exact expressions for frequency shift ... Read more

Generalized photo-thermo-elastic interaction in a semiconductor plate with two relaxation times
This study focuses on the effect of thermal relaxation times in a two-dimensional semiconductor medium by using eigenvalue approach. The formulation is applied under Green and Lindsay theory with two relaxation times. The bounding surface of the half-space is subjected to a heat flux with an exponentially decaying pulse and taken to be traction free. The variables solutions are obtained ... Read more

A study on fractional order theory in thermoelastic half-space under thermal loading
In this study, the effect of fractional order derivative on a two-dimensional problem due to thermal shock with weak, normal and strong conductivity is established. The governing equations are taken in the context of Green and Naghdi of type III model (GNIII model) under fractional order derivative. Based on the Laplace and exponential Fourier transformations with eigenvalues approach, the analytical ... Read more

Analytical and Numerical Solution of 2D Problem for Transversely Isotropic Generalized Thermoelastic Medium with Green-Naghdi Model II
In this paper, a comparison was made between the analytical and numerical solution of a two-dimensional problem for a transversely isotropic generalized thermoelastic medium. The study is carried out in the context of generalized thermoelasticity proposed by Green and Naghdi's theory of type II. The problem has been solved analytically using the normal mode method with the eigenvalue approach and ... Read more

Two-temperature photothermal interactions in a semiconducting material with a 3D spherical cavity
In this paper, a two-temperatures photothermoelastic interactions in an infinite semiconductor medium with a spherical cavity were studied using mathematical methods. The cavity internal surface is traction free and the carrier density is photogenerated by boundary heat flux with an exponentially decaying pulse. Laplace transform techniques are used to obtain the exact solution of the problem in the transformed domain ... Read more