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1
Content available remote Numerical studies for solving a free convection boundary-layer flow over a vertical plate
Othman M. I. A., Mahdy A. M. S.
Mechanics and Mechanical Engineering
|
2018
|
Vol. 22, nr 1
41--48
EN
In this paper, the aim of this study is to present a reliable combination of the shifted Legendre collocation method to approximate of the problem of free convection boundarylayer flow over a vertical plate as produced by a body force about a flat plate in the direction of the generating body force. The proposed method is based on replacement of the unknown function by truncated series of well known shifted Legendre expansion of functions. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shift Legendre coefficients. Thus, by solving this system of equations, the shifted Legendre coefficients are obtained. Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. The obtained results are in good agreement with those provided previously by the iterative numerical method. As a result, without taking or estimating missing boundary conditions, the shifted Legendre collocation method provides a simple, non-iterative and effective way for determining the solutions of nonlinear free convection boundary layer problems possessing the boundary conditions at infinity.
2
Content available remote The effect of initial stress on generalized thermoviscoelastic medium with voids and temperature-dependent properties under Green-Neghdi theory
Othman M. I. A., Fekry M.
Mechanics and Mechanical Engineering
|
2017
|
Vol. 21, nr 2
291--308
EN
The present paper aims to study the effect of initial stress on the 2-D problem of a homogeneous, isotropic, generalized thermo-viscoelastic material with voids in the context of Green-Naghdi theory. The modulus of elasticity is taken as a linear function of reference temperature. 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 (G-N II) and (G-N III) theory in the presence and absence of the initial stress and temperature-dependent properties.
3
Content available remote The effect of heat laser pulse on generalized thermoelasticity for micropolar medium
Othman M. I. A., Marin M.
Mechanics and Mechanical Engineering
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2017
|
Vol. 21, nr 4
797--811
EN
We introduced the coupled theory, Lord-Schulman theory with one relaxation time and Green-Lindsay theory with two relaxation times to study the influence of thermal loading due to laser pulse on generalized micropolar thermoelasticity. The bounding plane surface is heated by a non-Gaussian laser beam with the pulse duration of 8 ps. The methodology applied here is the use of normal mode analysis to solve the problem of thermal loading due to laser pulse to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and microrotation. The distributions of the considered variables are illustrated graphically. Comparisons are made with the results predicted by three theories in the presence of laser pulse and for different values of time.
4
Content available remote The effect of gravity and diffusion on micropolar thermoelasticity with temperature-dependent elastic medium under G-N theory
Othman M. I. A., Hilal M. I. M., Elmaklizi Y. D.
Mechanics and Mechanical Engineering
|
2017
|
Vol. 21, nr 3
657--677
EN
This article studies the effect of the gravity field and the diffusion on micropolar thermoelastic medium with dependence on the temperature properties. The analytic method used to obtain the exact formula of the physical quantities was the normal mode analysis. The comparisons established graphically in the presence and the absence of the gravity, the temperature-dependent properties, the diffusion and the micropolar in the context of two types of Green-Naghdi (G-N) theory II and III.
5
Content available remote Reaction of plane waves from a rotating magneto-thermoelastic medium with two-temperature and initial stress under three theories
Othman M. I. A., Abo-Dahab S. M., Alsebaey O. N. S.
Mechanics and Mechanical Engineering
|
2017
|
Vol. 21, nr 2
217--232
EN
The model of the equations of generalized magneto-thermoelasticity in an isotropic elastic medium with two-temperature under the effect initial stress is established. The entire elastic medium is rotated with a uniform angular velocity. The formulation is applied under three theories of generalized thermoelasticity: Lord-Shulman, Green-Lindsay, as well as the coupled theory. The Harmonic function is used to obtain the exact expressions for the considered variables. Some particular cases are also discussed in the context of the problem. We introduce the equations of the velocity of p-wave, T-wave and SV-wave. The boundary conditions for mechanical and Maxwell’s stresses and thermal insulated or isothermal are applied to determine the reflection coefficients for p-wave, T-wave and SV-wave. Some new aspects are obtained of the reflection coefficients and displayed graphically and the new conclusions are presented. Comparisons are also made with the results predicted by different theories (CT, L-S, G-L) in the presence of rotation, initial stress, magnetic field, as well as, the two-temperature parameter on the reflection of generalized thermos-elastic waves.
6
Content available remote Effect of thermal loading due to laser pulse on 3-d problem of micropolar thermoelastic solid with energy dissipation
Othman M. I. A., Atwa S. Y., Elwan A. W.
Mechanics and Mechanical Engineering
|
2017
|
Vol. 21, nr 3
679--701
EN
The aim of this paper is to introduce the Green-Naghdi (G-N) theory of type III (with energy dissipation) to study the effect of thermal loading due to laser pulse on generalized micropolar thermoelastic homogeneous isotropic medium in three dimensions. The normal mode analysis technique is used to solve the resulting non-dimensional equations of the problem. Numerical results for the displacement, thermal stress, strain, temperature, couple stresses and micro-rotation distributions are represented graphically to display the effect of the laser pulse on the resulting quantities. Comparisons are made within the theory in the presence and absence of the laser pulse.
7
Content available remote Effect of inclined load on micropolar theroelastic medium possessing cubic symmetry with energy dissipation
Othman M. I. A., Abo-Dahab S. M., Alosaimi H. A.
Mechanics and Mechanical Engineering
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2017
|
Vol. 21, nr 4
783--796
EN
The problem of the micropolar thermoelastic medium with (G-N) theory of types II (without energy dissipation) and type III (with energy dissipation) under the effect of the inclined load was investigated. The normal mode analysis is used to obtain the solution of the physical quantities. Comparisons are made between the results predicted by the (G-N) theory of type II and type III in different values of the angle of inclination.
8
Content available Effect of rotation on a semiconducting medium with two-temperatures under L-S theory
Othman M. I. A., Tantawi R. S., Eraki E. E. M.
Archives of Thermodynamics
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2017
|
Vol. 38, no. 2
101--122
EN
The model of the equations of generalized thermoelasticity in a semi-conducting medium with two-temperature is established. The entire elastic medium is rotated with a uniform angular velocity. The formulation is applied under Lord-Schulman theory with one relaxation time. The normal mode analysis is used to obtain the expressions for the considered variables. Also some particular cases are discussed in the context of the problem. Numerical results for the considered variables are obtained and illustrated graphically. Comparisons are also made with the results predicted in the absence and presence of rotation as well as two-temperature parameter.
9
Content available Effect of initial stress and gravity field on micropolar thermoelastic solid with microtemperatures
Othman M. I. A., Tantawi R. S., Hilal M. I. M.
Journal of Theoretical and Applied Mechanics
|
2016
|
Vol. 54 nr 3
847--857
EN
The purpose of the present article is the study of the effect of the gravity field on an initially stressed micropolar thermoelastic medium with microtemperatures. The analytical method used to obtain the formula of the physical quantities is the normal mode analysis. The comparisons are established graphically in the presence and the absence of gravity, initial stress and micropolar thermoelasticity. The main conclusions state that the gravity, initial stress and the micropolar thermoelasticity are effective physical operators on the variation of the physical quantities. The microtemperatures are very useful theory in the field of geophysics and earthquake engineering.
10
Content available remote Reflection of magneto-thermo-elastic waves from a rotating elastic half-space in generalized thermoelasticity under three theories
Othman M. I. A., Song Y.
Mechanics and Mechanical Engineering
|
2011
|
Vol. 15, nr 1
5-24
EN
The model of the equations of generalized magneto-thermoelasticity based on Lord-Shulman theory (LS) with one relaxation time, Green-Lindsay theory (GL) with two relaxation times, as well as the classical dynamical coupled theory (CD), is used to study the electro-magneto-thermoplastic interactions in a semi-infinite perfectly conducting solid. The entire elastic medium is rotating with a uniform angular velocity. There an initial magnetic field acts parallel to the plane boundary of the half-space. Reflection of magneto-thermoplastic waves under generalized thermoelasticity theory is employed to study the reflection of plane harmonic waves from a semi-infinite rotating elastic solid in a vacuum. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained. Similarly, the reflection coefficients ratios variation with the angle of incident under different conditions are shown graphically. Comparisons are made with the results predicted by the three theories in the presence and absence of rotation.
11
Content available remote The effect of thermal relaxation times on wave propagation of a micropolar thermoelastic medium with voids due to various sources
Othman M. I. A., Lotfy K.
International Journal of Applied Mechanics and Engineering
|
2011
|
Vol. 16, no 3
791-807
EN
A model of the equations of a two-dimensional problem with the deformation of a micropolar generalized thermoelastic medium with voids under the influence of various sources is formulated in the context of the Lord-Shulman, Green-Lindsay theories, as well as the classical dynamical coupled theory. The normal mode analysis is used to obtain the exact expressions of the displacement components, force stress, coupled stress, change in volume fraction field and temperature distribution. Numerical results are given and illustrated graphically when the volume source is applied. Comparisons are made with the results predicted by the three theories in the presence and absence of material constants due to voids.
12
Content available remote The effect of rotation and thermal shock on a perfect conducting elastic half-space in generalized magneto-thermoelasticity with two relaxation times
Othman M. I. A.
Mechanics and Mechanical Engineering
|
2010
|
Vol. 14, nr 1
31-55
EN
The propagation of electromagneto-thermoelastic disturbances produced by a thermal shock in a perfectly conducting elastic half-space when the entire elastic medium is rotating with a uniform angular velocity is investigated. The problem is in the context of the Green and Lindsay's generalized thermoelasticity with two relaxation times. There acts an initial magnetic field parallel to the plane boundary of the half-space. The medium deformed because of thermal shock, and due to the application of the magnetic field. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically. From the distributions, it can be found the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier's in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium. Comparisons are made wit h the results predicted by the coupled theory in present and absent rotation.
13
Content available remote Generalized electro-magneto-thermoelasticity in case of thermal shock plane waves for a finite conducting half-space with two relaxation times
Othman M. I. A.
Mechanics and Mechanical Engineering
|
2010
|
Vol. 14, nr 1
5-30
EN
The propagation of electromagneto-thermoelastic disturbances produced by a thermal shock in a finitely conducting elastic half-space is investigated. The formulation is applied to two-dimensional equations of generalized thermoelasticity Green and Lindsay's theory with two relaxation times. There acts an initial magnetic field parallel to the plane boundary of the half-space. The medium deformed because of thermal shock and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the medium. The Maxwell's equations are formulated and the electromagneto-thermoelastic coupled governing equations are established. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically for different values of times. From the distributions, it can be found the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier's in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium.
14
Content available remote Fundamental solution of plane waves in generalized thermo-microstretch elastic half-space
Othman M. I. A., Lotfy Kh., Farouk R. M.
International Journal of Applied Mechanics and Engineering
|
2010
|
Vol. 15, no 1
175-197
EN
A general model of equations of generalized thermo-microstretch for a homogeneous isotropic elastic half space is given. The formulation is applied to generalized thermoelasticity theories, the Lord-Shulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and microstress distribution. The variations of the variables through the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence and absence of microstretch constants and between the three theories for two different times.
15
Content available remote The Thermal Relaxation Effect on 2-D Problems of the Generalized Linear Thermo-Viscoelasticity
Othman M. I. A.
Mechanics and Mechanical Engineering
|
2009
|
Vol. 13, nr 1
45-62
EN
In this paper we introduced the normal mode analysis for two-dimensional problems of the generalized linear thermo-viscoelasticity with one relaxation time. The exact expressions for the temperature distribution, the displacement components and the stress are obtained. The resulting formulation is applied to three different concrete problems. The first deals with a thick plate subjected to a time-dependent heat source on each face. The second concerns to the case of a heated punch moving across the surface of a semi-infinite thermo-viscoelastic half-space subjected to appropriate boundary conditions and the third problem deals with a plate with thermo-isolated surfaces subjected to a time-dependent compression. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory.
16
Content available remote Generalized Thermo-Viscoelasticity under Three Theories
Othman M. I. A.
Mechanics and Mechanical Engineering
|
2009
|
Vol. 13, nr 1
25-44
EN
The model of the equations of the two-imensional generalized thermo-viscoelasticity based on Lord-Shultnan (L-S), Green and Lindsay (G-L) and Classical dynamical-coupled (CD) theories are studied. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, displacement components, and the thermal stresses. The resulting formulation is applied to two different concrete problems. The first concerns to the case of a heat, punch across the surface of a semi-infinite thermo-viscoelastic half-space subject to appropriate boundary conditions. The second deals with a plate with thermo-isolated surfaces subjected to a time-dependent compression. A comparison is carried out between temperature, displacement and stress as calculated for each problem from view of the different theories of generalized thermo-viscoelasticity. Numerical results are given and illustrated graphically. Comparisons are made with the results predicted by three theories. The analysis presented in this paper is more general than any previous investigation.
17
Content available remote Effect of Rotation in Case of 2-D Problem of the Generalized Thermo-viscoelasticity with Two Relaxation Times
Othman M. I. A.
Mechanics and Mechanical Engineering
|
2009
|
Vol. 13, nr 2
105-127
EN
In this paper, a two-dimensional problem of thermoviscoelasticity with two relaxation times when the entire medium rotates with a uniform angular velocity is studied. The normal mode analysis is used to obtain the exact expressions for the temperature, displacement and thermal stress components. The resulting formulation is applied to the case of a thick plate subjected to a time-dependent heat source on each face. Numerical results are given and illustrated graphically. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermoelasticity with two relaxation times in the absence of rotation and for different values of time.
18
Content available remote Thermal Instability in a Rotating Micropolar Viscoelastic Fluid Layer Under the Effect of Electric Field
Othman M. I. A., Zaki S. A.
Mechanics and Mechanical Engineering
|
2008
|
Vol. 12, nr 2
171-184
EN
The problem of onset of convective instability in a dielectric micropolar viscoelastic fluid (Walters' liquid B') heated from below confined between two horizontal plates under the simultaneous action of the rotation of the system, vertical temperature gradient, one relaxation time and vertical electric field is considered. Linear stability theory is used to derive an eigenvalue of twelve order, and an exact eigenvalue equation for a neutral instability is obtained. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the eigenvalue relationship from which various critical values are determined in detail. Critical Rayleigh heat numbers and wave number for the onset of instability are presented graphically as a function of rotation at a certain value of the Prandtl number, for various values of the relaxation time, the Rayleigh electric number, the elastic parameter and micropolar parameters.
19
Content available remote Efect of Reference Temperature on the Modulus of Elasticity in Case of 2-D Generalized Thermal Shock Problem for a Half-Space
Othman M. I. A.
Mechanics and Mechanical Engineering
|
2007
|
Vol. 11, nr 1
49-63
EN
The model of the equations of two-dimensional coupled problem in thermo-elasticity for a thermally half-space solid whose surface is subjected to a thermal shock is established. The problem is in the context of the Green and Lindsay's generalized thermoelasticity theory with two relaxation times in an isotropic medium with the modulus of elasticity being dependent on the reference temperature. The normal mode analysis is used to obtain the exact expressions for the temperature, the displacement and thermal stress components. The resulting formulation is applied to two kinds of boundary conditions. Numerical results are illustrated graphically for each case considered. Comparison is carried out with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature.
20
Content available remote Generalized Thermoelasticity Plane Waves in Rotating Media with Thermal Relaxation under the Temperature Dependent Properties
Othman M. I. A.
Mechanics and Mechanical Engineering
|
2005
|
Vol. 9, nr 2
89--110
EN
A two-dimensional coupled problem in generalized thermoelasticity for rotating media under the temperature dependent properties is studied. The problem is in the context of the Lord-Shulman's theory with one relaxation time. The normal mode analysis is used to obtain the expressions for the temperature distribution, displacement components and thermal stresses. The resulting formulation is applied to two different problems. The first concerns the case of a heat punch moving across the surface of a semi-infinite thermoelastic half-space subjected to appropriate boundary conditions. The second deals with a thick plate subject to a time-dependent heat source on each face. Numerical results are illustrated graphically for each problem considered. Comparisons are made with the results obtained predicted by the two theories in case of absence of rotation.
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