scholarly journals One-Dimensional Problem of a Conducting Viscous Fluid with One Relaxation Time

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
Angail A. Samaan
Keyword(s):  
Relaxation Time ◽  
Thermal Relaxation ◽  
Heat Sources ◽  
One Dimensional ◽  
Boundary Layer Equations ◽  
Laplace Transform Technique ◽  
The Matrix ◽  
The Laplace Transform ◽  
Magnetohydrodynamic Model ◽  
Plane Distribution

We introduce a magnetohydrodynamic model of boundary-layer equations for conducting viscous fluids. This model is applied to study the effects of free convection currents with thermal relaxation time on the flow of a viscous conducting fluid. The method of the matrix exponential formulation for these equations is introduced. The resulting formulation together with the Laplace transform technique is applied to a variety problems. The effects of a plane distribution of heat sources on the whole and semispace are studied. Numerical results are given and illustrated graphically for the problem.

State space approach to one-dimensional magneto-thermoelasticity under the Green–Naghdi theories

2009 ◽  
Vol 87 (8) ◽  
pp. 867-878 ◽  
Author(s):  
Magdy A. Ezzat ◽  
A. S. El-Karamany ◽  
A.A. Bary
Keyword(s):  
State Space ◽  
Generalized Thermoelasticity ◽  
Heat Sources ◽  
State Space Approach ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
Isotropic Media ◽  
The Laplace Transform ◽  
Space Approach ◽  
Coupled Theory

A model of the equations of generalized magneto-thermoelasticity for perfectly conducting isotropic media is given. The formulation is applied to the generalized thermoelasticity theories: Green–Naghdi of type II and type III as well as to the dynamic coupled theory. The state space approach is adopted for the solution of one-dimensional problems in the absence of heat sources with time-dependent heating on the boundary. The Laplace-transform technique is used. Numerical results are given and illustrated graphically employing numerical method for the inversion of the Laplace transforms. Comparisons are made with the results predicted by the three theories.

scholarly journals Exact Solution of Thermoelastic Problem for a One-Dimensional Bar without Energy Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
A. M. Abd El-Latief ◽  
S. E. Khader
Keyword(s):  
Exact Solution ◽  
Relaxation Time ◽  
Thermal Stress ◽  
Energy Dissipation ◽  
Heat Source ◽  
Half Space ◽  
Time Dependent ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Without Energy Dissipation

We consider a homogeneous isotropic thermoelastic half-space in the context of the theory of thermoelasticity without energy dissipation. There are no body forces or heat source acting on the half-space. The surface of the half-space is affected by a time dependent thermal shock and is traction free. The Laplace transform with respect to time is used. The inverse transforms are obtained in an exact manner for the temperature, thermal stress, and displacement distributions. These solutions are represented graphically and discussed for several cases of the applied heating. Comparison is made between the predictions here and those of the theory of thermoelasticity with one relaxation time.

Thermodiffusion with two time delays and Kernel functions

2016 ◽  
Vol 23 (2) ◽  
pp. 195-208 ◽  
Author(s):  
Ahmed S El-Karamany ◽  
Magdy A Ezzat ◽  
Alaa A El-Bary
Keyword(s):  
Laplace Transform ◽  
Kernel Functions ◽  
Transform Domain ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Isotropic Elastic Medium ◽  
Time Variations ◽  
With Memory

The present work is concerned with the investigation of disturbances in a homogeneous, isotropic elastic medium with memory-dependent derivatives (MDDs). A one-dimensional problem is considered for a half-space whose surface is traction free and subjected to the effects of thermodiffusion. For treatment of time variations, the Laplace-transform technique is utilized. The theories of coupled and of generalized thermoelastic diffusion with one relaxation time follow as limit cases. A direct approach is introduced to obtain the solutions in the Laplace transform domain for different forms of kernel functions and time delay of MDDs, which can be arbitrarily chosen. Numerical inversion is carried out to obtain the distributions of the considered variables in the physical domain and illustrated graphically. Some comparisons are made and shown in figures to estimate the effects of MDD parameters on all studied fields.

scholarly journals Interactions due to Moving Heat Sources in Generalized Thermoelastic Half-Space using L-S Model

2013 ◽  
Vol 18 (3) ◽  
pp. 815-831 ◽  
Author(s):  
N. Sarkar ◽  
A. Lahiri
Keyword(s):  
Half Space ◽  
Heat Sources ◽  
Dimensional Problem ◽  
Eigenvalue Approach ◽  
One Dimensional ◽  
Coupled Equations ◽  
The Laplace Transform ◽  
Moving Plane ◽  
Generalized Thermoelastic ◽  
S Model

Abstract A one-dimensional problem for a homogeneous, isotropic and thermoelastic half-space subjected to a moving plane of heat source on the boundary of the space, which is traction free, is considered in the context of Lord- Shulaman model (L-S model) of thermoelasticity. The Laplace transform and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled equations. Numerical results for the temperature, thermal stress, and displacement distributions are represented graphically and discussed

State space formulation for boundary-layer magneto-hydrodynamic free convection flow with one relaxation time

2002 ◽  
Vol 80 (10) ◽  
pp. 1157-1174 ◽  
Author(s):  
M A Ezzat ◽  
A A Samaan ◽  
A Abd-El Bary
Keyword(s):  
Boundary Layer ◽  
Relaxation Time ◽  
State Space ◽  
Boundary Layer Equation ◽  
Convection Flow ◽  
Heat Sources ◽  
Space Problem ◽  
Whole Space ◽  
Space Formulation ◽  
Plane Distribution

We introduce a magnetohydrodynamic model of a boundary-layer equation for a conducting viscous fluid. The state space approach is adopted for one-dimensional problems including heat sources with one relaxation time. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semi-space problem with a plane distribution of heat sources located inside the fluid. Numerical results for the velocity, temperature, and induced-magnetic- and induced-electric-field distributions are given and illustrated graphically for both problems. PACS No.: 47.65+a

Thermoelasticity When the Material Coupling Parameter Equals Unity

1965 ◽  
Vol 32 (2) ◽  
pp. 378-382 ◽  
Author(s):  
O. W. Dillon
Keyword(s):  
Laplace Transform ◽  
Constant Velocity ◽  
Coupling Parameter ◽  
Step Function ◽  
Surface Strain ◽  
Coupled Thermoelasticity ◽  
Velocity Impact ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Analytical solutions of three problems in coupled thermoelasticity are presented for the case when the material coupling parameter equals unity. The problems considered are: (a) Danilovskaya’s problem of a step function in temperature at the surface; (b) a step function in surface strain; and (c) constant velocity impact. Solutions are presented for the case of thin bars (one-dimensional stress) and are obtained by the Laplace-transform technique. There is great simplification in the equations when the material coupling parameter equals unity which permits the straightforward inversion of the transformed solutions. The results demonstrate significant deviations from the corresponding uncoupled solutions.

On three models of magneto-hydrodynamic free-convection flow

2009 ◽  
Vol 87 (12) ◽  
pp. 1213-1226 ◽  
Author(s):  
Magdy A. Ezzat ◽  
A. A. El-Bary
Keyword(s):  
Convection Flow ◽  
Heat Sources ◽  
Space Problem ◽  
State Space Approach ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Whole Space ◽  
Plane Distribution ◽  
The One ◽  
Space Approach

In this work, we introduce a model of the boundary-layer equations of a generalized thermofluid for an electrically conducting pourous medium in the presence of a constant magnetic field. This model is applied to each generalization, Cattaneo theory with one relaxation time, Chandrasekharaiah–Tzou theory, as well as classical Fourier law. The state space approach developed by Ezzat (Can. J. Phys. 86, 1241 (2008)), is adopted for the one-dimensional problems including heat sources. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semi-space problem with a plane distribution of heat sources located inside the fluid. Numerical results for the velocity, temperature, and induced-magnetic and electric field distributions are given and illustrated graphically for both problems. The comparisons are made for all functions with the results obtained in the three theories.

An Analytical Solution for Boundary Layer Flows Over a Moving-Flat Porous Plate With Viscous Dissipation

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
C. J. Toki
Keyword(s):  
Boundary Layer ◽  
Viscous Dissipation ◽  
Porous Plate ◽  
Fluid Temperature ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
Dissipation Parameter ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Layer Flow

The problem of boundary layer flow of an incompressible fluid over a moving porous flat plate is investigated, by taking into account the heat due to viscous dissipation. The governing boundary layer equations of this flow field were solved analytically using the Laplace transform technique. These new exact analytical solutions for velocity and temperature were obtained with arbitrary Prandtl number and dissipation parameter (or Eckert number Ec). The corresponding solutions for nonporous plate are discussed. Applying numerical values into the analytical expressions of the temperature and heat transfer coefficient, we also discussed the effects of the dissipation parameter in the cases of water, gas, and ammonia flow. We can finally deduce that the fluid temperature of the present problem will increase in the case of viscous dissipation with positive Ec, but this temperature will decrease with negative Ec.

scholarly journals Free convection flow of conducting micropolar fluid with thermal relaxation including heat sources

2004 ◽  
Vol 2004 (4) ◽  
pp. 271-292 ◽  
Author(s):  
Magdy A. Ezzat
Keyword(s):  
Free Convection ◽  
Micropolar Fluid ◽  
Vertical Plane ◽  
Thermal Relaxation ◽  
Convection Flow ◽  
Heat Sources ◽  
Free Convection Flow ◽  
Space Technique ◽  
Whole Space ◽  
Plane Distribution

The present work is concerned with unsteady free convection flow of an incompressible electrically conducting micropolar fluid, bounded by an infinite vertical plane surface of constant temperature. A uniform magnetic field acts perpendicularly to the plane. The state space technique is adopted for the one-dimensional problems including heat sources with one relaxation time. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semispace problem with a plane distribution of heat sources located inside the fluid. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the temperature, the velocity, and the angular velocity distributions are given and illustrated graphically for the problems considered.

Correlating Blocking Temperatures in Single Molecule Magnets with Raman Relaxation

2018 ◽  
Author(s):  
Marcus J. Giansiracusa ◽  
Andreas Kostopoulos ◽  
George F. S. Whitehead ◽  
David Collison ◽  
Floriana Tuna ◽  
...  
Keyword(s):  
Relaxation Time ◽  
Single Molecule ◽  
Energy Barrier ◽  
Thermal Relaxation ◽  
Relaxation Mechanism ◽  
Blocking Temperature ◽  
Single Molecule Magnets ◽  
Single Molecule Magnet ◽  
Key Parameter

We report a six coordinate DyIII single-molecule magnet<br>(SMM) with an energy barrier of 1110 K for thermal relaxation of<br>magnetization. The sample shows no retention of magnetization<br>even at 2 K and this led us to find a good correlation between the<br>blocking temperature and the Raman relaxation regime for SMMs.<br>The key parameter is the relaxation time (𝜏<sub>switch</sub>) at the point where<br>the Raman relaxation mechanism becomes more important than<br>Orbach.

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