Two-temperature theory in generalized magneto-thermo-viscoelasticity

2009 ◽  
Vol 87 (4) ◽  
pp. 329-336 ◽  
Author(s):  
Magdy A. Ezzat ◽  
Alaa Abd El Bary ◽  
Ahmed S. El Karamany
Keyword(s):  
Magnetic Field ◽  
Specific Problem ◽  
Relaxation Times ◽  
Numerical Approach ◽  
Dimensional Model ◽  
State Space Approach ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Two Temperature ◽  
Space Approach

A one-dimensional model of the two-temperature generalized magneto-viscoelasticity with two relaxation times in a perfect conducting medium is established. The state space approach is adopted for the solution of one-dimensional problems for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a specific problem of a half-space subjected to thermal shock and traction-free surface. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Some comparisons have been shown in figures to estimate the effects of the temperature discrepancy and the applied magnetic field.

MHD free convection flow of a micropolar fluid past a vertical porous plate

2002 ◽  
Vol 80 (12) ◽  
pp. 1661-1673 ◽  
Author(s):  
K A Helmy ◽  
H F Idriss ◽  
S E Kassem
Keyword(s):  
Micropolar Fluid ◽  
Porous Plate ◽  
Infinite Plate ◽  
Numerical Approach ◽  
Convection Flow ◽  
Heated Plate ◽  
Governing Equations ◽  
State Space Approach ◽  
The Laplace Transform ◽  
Space Approach

The present work is concerned with the unsteady flow of an incompressible, viscous, conducting micropolar fluid, through a porous medium, over an infinite plate that is started into motion in its own plane by an impulse. A uniform magnetic field acts in a direction perpendicular to the plate. The governing equations are solved using a state space approach and the inversion of the Laplace transform is carried out, using a numerical approach. The technique is applied to a heated-plate problem and to a problem pertaining to a plate under uniform heating. Numerical results concerning temperature (for both problems), velocity, and microrotation are given and are illustrated graphically. PACS Nos.: 47.00, 65.00, 47.50, 76.00

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.

Two-Temperature Generalized Thermo-Elastic Medium Thermally Excited by Time Exponentially Decaying Laser Pulse

2016 ◽  
Vol 16 (03) ◽  
pp. 1450102 ◽  
Author(s):  
Hamdy M. Youssef ◽  
A. A. El-Bary
Keyword(s):  
Laser Pulse ◽  
Absorption Coefficient ◽  
Transformation Method ◽  
State Space Approach ◽  
Closed Form Solutions ◽  
Riemann Sum ◽  
Temperature Parameter ◽  
Laplace Transformation Method ◽  
Two Temperature ◽  
Space Approach

This paper deals with a two-temperature thermoelastic material subjected to a laser heating pulse as the heat source. Closed form solutions for the temperature and stress fields due to time exponentially decaying laser pulse are presented using the state-space approach. The Laplace transformation method is employed in deriving the governing equations. The inversion of Laplace transform is obtained numerically by using the Riemann-sum approximation method. The results have been presented in figures to show the effect of the time exponentially decaying laser pulse, the two-temperature parameter and the absorption coefficient on all the fields studied. The results show that the two-temperature parameter and the absorption coefficient parameter have significant effects on all the field parameters studied.

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