scholarly journals An Analytical Solution for Effect of Magnetic Field and Initial Stress on an Infinite Generalized Thermoelastic Rotating Nonhomogeneous Diffusion Medium

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
S. R. Mahmoud
Keyword(s):  
Magnetic Field ◽  
Relaxation Time ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Initial Stress ◽  
Chemical Potential ◽  
Thermoelastic Diffusion ◽  
Generalized Thermoelastic ◽  
Analytical Expressions ◽  
And Diffusion

The problem of generalized magneto-thermoelastic diffusion in an infinite rotating nonhomogeneity medium subjected to certain boundary conditions is studied. The chemical potential is also assumed to be a known function of time at the boundary of the cavity. The analytical expressions for the displacements, stresses, temperature, concentration, and chemical potential are obtained. Comparison was made between the results obtained in the presence and absence of diffusion. The results indicate that the effect of nonhomogeneity, rotation, magnetic field, relaxation time, and diffusion is very pronounced.

scholarly journals A Two-Dimensional Generalized Electromagnetothermoelastic Diffusion Problem for a Rotating Half-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Jingrui Zhang ◽  
Yanyan Li
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Half Space ◽  
Chemical Potential ◽  
Diffusion Problem ◽  
Two Dimensional ◽  
Constant Intensity ◽  
Thermoelastic Wave ◽  
Thermoelastic Diffusion ◽  
Nondimensional Temperature

In the context of the theory of generalized thermoelastic diffusion, a two-dimensional generalized electromagnetothermoelastic problem with diffusion for a rotating half-space is investigated. The rotating half-space is placed in an external magnetic field with constant intensity and its bounding surface is subjected to a thermal shock and a chemical potential shock. The problem is formulated based on finite element method and the derived finite element equations are solved directly in time domain. The nondimensional temperature, displacement, stress, chemical potential, concentration, and induced magnetic field are obtained and illustrated graphically. The results show that all the considered variables have a nonzero value only in a bounded region and vanish identically outside this region, which fully demonstrates the nature of the finite speeds of thermoelastic wave and diffusive wave.

Method of regularized sources for axisymmetric Stokes flow problems

2016 ◽  
Vol 26 (3/4) ◽  
pp. 1226-1239 ◽  
Author(s):  
Kai Wang ◽  
Shiting Wen ◽  
Rizwan Zahoor ◽  
Ming Li ◽  
Božidar Šarler
Keyword(s):  
Analytical Solution ◽  
Fundamental Solution ◽  
Boundary Conditions ◽  
Stokes Flow ◽  
Regularization Parameter ◽  
Fine Grid ◽  
Content Type ◽  
Flow Problems ◽  
Singular Source ◽  
Analytical Expressions

Purpose – The purpose of this paper is to find solution of Stokes flow problems with Dirichlet and Neumann boundary conditions in axisymmetry using an efficient non-singular method of fundamental solutions that does not require an artificial boundary, i.e. source points of the fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and velocity represents analytical solution of the flow due to a singular Dirac delta source in infinite space. Design/methodology/approach – Instead of the singular source, a non-singular source with a regularization parameter is employed. Regularized axisymmetric sources were derived from the regularized three-dimensional sources by integrating over the symmetry coordinate. The analytical expressions for related Stokes flow pressure and velocity around such regularized axisymmetric sources have been derived. The solution to the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary. The intensities of the sources are chosen in such a way that the solution complies with the boundary conditions. Findings – An axisymmetric driven cavity numerical example and the flow in a hollow tube and flow between two concentric tubes are chosen to assess the performance of the method. The results of the newly developed method of regularized sources in axisymmetry are compared with the results obtained by the fine-grid second-order classical finite difference method and analytical solution. The results converge with a finer discretization, however, as expected, they depend on the value of the regularization parameter. The method gives accurate results if the value of this parameter scales with the typical nodal distance on the boundary. Originality/value – Analytical expressions for the axisymmetric blobs are derived. The method of regularized sources is for the first time applied to axisymmetric Stokes flow problems.

FINITE ELEMENT METHOD TO A GENERALIZED ELECTROMAGNETO-THERMOELASTIC PROBLEM WITH DIFFUSION

2012 ◽  
Vol 04 (04) ◽  
pp. 1250046 ◽  
Author(s):  
TIANHU HE ◽  
YANYAN LI ◽  
SHUANHU SHI
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Half Space ◽  
Chemical Potential ◽  
Thermoelastic Problem ◽  
Constant Intensity ◽  
Thermoelastic Wave ◽  
Thermoelastic Diffusion ◽  
Element Method

In the context of the theory of generalized thermoelastic diffusion, a two-dimensional generalized electromagneto-thermoelastic problem with diffusion for a half-space is investigated. The half-space is placed in an external magnetic field with constant intensity and its bounding surface is subjected to a thermal shock and a chemical potential shock. The governing equations of the problem are formulated and solved numerically by means of finite element method. The derived finite element equations are solved directly in time domain. The nondimensional temperature, displacement, stress, chemical potential, concentration and induced magnetic field are obtained and illustrated graphically. The results show that all the considered variables have a nonzero value only in a bounded region and vanish identically outside this region, which fully demonstrates the nature of the finite speeds of thermoelastic wave and diffusive wave.

Effect of Magnetic Field on Generalized Thermo-Viscoelastic Diffusion Medium with Voids

2016 ◽  
Vol 16 (07) ◽  
pp. 1550033 ◽  
Author(s):  
Mohamed I. A. Othman ◽  
Montaser Fekry
Keyword(s):  
Magnetic Field ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Physical Domain ◽  
Specific Material ◽  
Analytical Expressions ◽  
And Diffusion ◽  
Physical Quantities ◽  
The Magnetic Field

The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic, generalized thermo-viscoelastic diffusion material with voids under the influence of magnetic field. The formulation is applied to the generalized thermoelasticity theory under the Lord–Shulman and the classical dynamical coupled theories. The analytical expressions for the physical quantities are obtained in the physical domain by using the normal mode analysis. These expressions are calculated numerically for a specific material and explained graphically. Comparisons are made with the results predicted by the Lord–Shulman and the coupled theories in the presence and absence of the magnetic field and diffusion.

scholarly journals A RECTANGULAR PLATE ON A TWO-PARAMETER ELASTIC BASE: THE ANALYTICAL SOLUTION

2017 ◽  
Vol 17 (8) ◽  
pp. 128-133
Author(s):  
A.A. Bolshakov
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Double Series ◽  
Elastic Base ◽  
Elastic Support ◽  
Analytical Expressions ◽  
Two Parameter

In the paper the approximate solution for a problem of a rectangular plate on a two-parameter elastic base is suggested. The double series of beam functions satisfying elastic support boundary conditions are constructed. The analytical expressions for series function coefficients are obtained.

scholarly journals Solution of Lord-Shulmans and dual-phase-lag theories problem on a photothermal rotational semiconductor medium with voids and initial stress

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 59-68
Author(s):  
Hammad Alotaibi
Keyword(s):  
Boundary Conditions ◽  
Initial Stress ◽  
Carrier Density ◽  
Equations Of Motion ◽  
Phase Lag ◽  
Dual Phase ◽  
Stress Components ◽  
Differential Equa ◽  
Generalized Thermoelastic ◽  
Thermoelastic Theory

This paper discusses a photo-thermal rotational semiconductor medium with ini?tial stress, and voids by considering two thermoelastic theories: Lord-Shulman and Dual-Phase-Lag models. The equations of motion, temperature, voids, and photothermal have been investigated under two generalized thermoelastic theory. The technique of normal mode has been applied to solve the differential equa?tions system with appropriate boundary conditions. Quantities of physical interest such as displacement, stress components, concentration, temperature, and carrier density are calculated and displayed graphically to demonstrate the effect of the external parameters. The obtained results, by using the two theories, show that the dual-phase-lag theory gives an origin results comparing with obtained results by Lord-Shulman theory. By neglecting the initial stress and voids, and considering the only dual-phase-lag theory, then the results obtained in this paper are deduced to the results of Abbas et al. [1].

Sign in / Sign up

Export Citation Format

Share Document