Prof. Dr. Ibrahim A. Abbas

Professor - Department of Mathematics

Faculty of science

Address: Sohag University, Egypt.

307

Analytical-Numerical solution of thermoelastic interactions in a semi-infinite medium with one relaxation time

2015 | Keywords Thermoelasticity, relaxation time, Analytical-Numerical Solution,

Analytical and numerical solutions are two basic tools in the study of thermoelastic interactions problems in anisotropic media. This paper is devoted to a study of the thermoelastic interactions in a semi-infinite medium in the context of the theory of generalized thermoelasticity with one relaxation time (Lord and Shulman's theory). The governing equations are expressed in Laplace transform domain and ... Read more

Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity

2015 | Keywords spherical cavity, eigenvalue approach, fractional order theory, Thermoelastic Diffusion,

$Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity$

In this work, we study a problem in a fractional order theory of thermoelastic diffusion in an infinite medium with a spherical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity. The chemical potential is assumed a known function of time on the bounding cavity. The form of vector–matrix differential ... Read more

Thermoelastic interaction in a thermally conducting cubic crystal subjected to ramp-type heating

2015 | Keywords cubic crystal, Thermoelastic, finite element method,

In this paper, the thermoelastic interactions in a homogeneous, thermally conducting cubic crystal, elastic half-plane has been studied. A linear temperature ramping function is used to more realistically model. The general solution obtained is applied to a specific problem of a half space subjected to ramp-type heating. The components of displacement, stresses, and temperature distribution are obtained by applying a ... Read more

The effect of magnetic field on thermal shock problem for a fiber-reinforced anisotropic half-space using Green-Naghdi's theory

2015 | Keywords magnetic field, Fiber-Reinforced, finite element method, Thermoelasticity,

This article presents a two-dimensional problem of generalized thermoelasticity for a fiber-reinforcement anisotropic half-space under a thermal shock at its upper surface. The effects of initial stress and rotation are both studied. Green and Naghdi's theory of thermoelasticity is employed to study the present problem. The inclusion of reinforcement anisotropic elastic parameter is made and two additional terms are added ... Read more

Thermoelastic interactions in an isotropic unbounded medium due to moving heat source using GNIII model

2015 | Keywords heat source, unbounded medium, Thermoelastic, GNIII model, moving heat source,

In this work, we study a problem of thermoelastic interaction due to moving heat source in an isotropic infinite medium under Green and Naghdi model of type III (GNIII). The form of vector-matrix differential equation in the Laplace transform domain, the basic equations have been written, which is then solved by an eigenvalue technique. The analytical solution in the Laplace ... Read more

Vibrational analysis for an axially moving microbeam with two temperatures

2015 | Keywords microbeam, axially moving, wo temperatures,

In this article, the effect of two temperatures on an axially moving microbeam subjected to ramp-type heating is studied. The generalized thermoelasticity theory with one relaxation time model is used. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique, the inversion of Laplace transform is done numerically. Some comparisons have been shown in figures ... Read more

Two-dimensional fractional order generalized thermoelastic porous material

2015 | Keywords porous material, fractional order, Thermoelastic,

$Two-dimensional fractional order generalized thermoelastic porous material$

In the work, a two-dimensional problem of a porous material is considered within the context of the fractional order generalized thermoelasticity theory with one relaxation time. The medium is assumed initially quiescent for a thermoelastic half space whose surface is traction free and has a constant heat flux. The normal mode analysis and eigenvalue approach techniques are used to solve ... Read more

Fractional Order Theory of Thermoelastic Diffusion Problem for an Infinite Medium with Cylindrical Cavity

2015 | Keywords Cylindrical Cavity, Thermoelastic Diffusion, fractional order theory,

The fractional order theory of generalized thermoelastic diffusion with relaxation times, in the context of Lord and Shulman theory, is used to investigate the thermoelastic diffusion problem in an infinite medium with a cylindrical cavity. The surface of cavity is taken to be traction free and subjected to heating. The chemical potential is assumed a known function of time on ... Read more

Behavior of Cesaro Means of Energy Components for Non-Simple Thermoelastic Bodies

2015 | Keywords Cesaro Means, Thermoelastic Bodies,

The mixed initial boundary value problem in the context of non-simple thermoelastic materials is approached. The energy components of the solution to this problem are associated with so called Cesaro means. The main result of this study consists in demonstrating that Cesaro means of the kinetic and strain energies become asymptotically equal as time tends to infinity. Read more

Interaction Due to Thermal Source in Micropolar Thermoelastic Diffusion Medium

2015 | Keywords Thermal Source, Thermoelastic Diffusion, micropolar,

In present study, the deformation in a micropolar thermoelastic diffusion medium due to thermal source by the use of finite element method (FEM) is investigated in the context of Lord-Shulman (L-S) theory of Thermoelasticity. A special type of sources have been taken to show the utility of the approach. The components of displacement, stress, microrotation, temperature change and mass concentration ... Read more

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AddressSohag University, Egypt.
Phone934592075
Fax934592075
Emailibrabbas7@science.sohag.edu.eg

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