One-dimensional problem for infinitely long annular cylinder in the context of fractional order theory of thermoelasticity

2016 ◽  
Vol 96 (12) ◽  
pp. 1482-1489 ◽  
Author(s):  
Eman M. Hussein
Keyword(s):  
Fractional Order ◽  
Order Theory ◽  
Dimensional Problem ◽  
One Dimensional

scholarly journals A One-Dimensional Thermoelastic Problem due to a Moving Heat Source under Fractional Order Theory of Thermoelasticity

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Tianhu He ◽  
Ying Guo
Keyword(s):  
Heat Source ◽  
Laplace Transform ◽  
Fractional Order ◽  
Order Parameter ◽  
Order Theory ◽  
Numerical Inversion ◽  
Moving Heat Source ◽  
Dimensional Problem ◽  
Governing Equations ◽  
One Dimensional

The dynamic response of a one-dimensional problem for a thermoelastic rod with finite length is investigated in the context of the fractional order theory of thermoelasticity in the present work. The rod is fixed at both ends and subjected to a moving heat source. The fractional order thermoelastic coupled governing equations for the rod are formulated. Laplace transform as well as its numerical inversion is applied to solving the governing equations. The variations of the considered temperature, displacement, and stress in the rod are obtained and demonstrated graphically. The effects of time, velocity of the moving heat source, and fractional order parameter on the distributions of the considered variables are of concern and discussed in detail.

scholarly journals A Study on Fractional Order Thermoelastic Half Space

2020 ◽  
Vol 25 (4) ◽  
pp. 191-202
Author(s):  
Sourov Roy ◽  
Abhijit Lahiri
Keyword(s):  
Half Space ◽  
Fractional Order ◽  
Equations Of Motion ◽  
Generalized Thermoelasticity ◽  
Dimensional Problem ◽  
Governing Equations ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Eigen Value ◽  
The Laplace Transform

AbstractIn this paper, we consider a one dimensional problem on a fractional order generalized thermoelasticity in half space subjected to an instantaneous heat source. The Laplace transform as well as eigen value approach techniques are applied to solve the governing equations of motion and heat conduction. Closed form solutions for displacement, temperature and stress are obtained and presented graphically.

Fractional order theory of a perfect conducting thermoelastic medium

2011 ◽  
Vol 89 (3) ◽  
pp. 311-318 ◽  
Author(s):  
Magdy A. Ezzat ◽  
Ahmed S. El-Karamany
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Mathematical Model ◽  
Heat Flux ◽  
Fractional Order ◽  
Order Parameter ◽  
Order Theory ◽  
Thermoelastic Medium ◽  
One Dimensional ◽  
Electric And Magnetic Fields

In this work, a new mathematical model of magneto-thermoelasticity theory is constructed in the context of a new consideration of heat conduction law with time-fractional order. This model is applied to a one-dimensional application for a perfect conducting half-space of elastic material, which is thermally shocked in the presence of magnetic field. Laplace transforms and state-space techniques (Ezzat. Can. J. Phys. 86, 1242, (2008)) will be used to obtain the general solution for any set of boundary conditions. According to numerical results and graphs, it is found that introducing a fractional derivative of order α has a significant effect on the temperature, stress, and heat flux distributions as well as the induced electric and magnetic fields; the curves are smoother in the case of 0 < α < 1 due to weak thermal conductivity. Some comparisons are made and shown in figures to estimate the effects of the fractional order parameter on all the studied fields.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

Fractional-Order Viscoelasticity in One-Dimensional Blood Flow Models

2014 ◽  
Vol 42 (5) ◽  
pp. 1012-1023 ◽  
Author(s):  
Paris Perdikaris ◽  
George Em. Karniadakis
Keyword(s):  
Blood Flow ◽  
Fractional Order ◽  
One Dimensional ◽  
Flow Models ◽  
Blood Flow Models
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