scholarly journals Fractional-Order Thermoelastic Wave Assessment in a Two-Dimensional Fiber-Reinforced Anisotropic Material

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1609
Author(s):  
Samah Horrigue ◽  
Ibrahim A. Abbas
Keyword(s):  
Fractional Order ◽  
Time Derivative ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
Fiber Reinforced ◽  
Thermoelastic Wave ◽  
Practical Applications ◽  
Fractional Time Derivative ◽  
Fiber Reinforced Material

The present work is aimed at studying the effect of fractional order and thermal relaxation time on an unbounded fiber-reinforced medium. In the context of generalized thermoelasticity theory, the fractional time derivative and the thermal relaxation times are employed to study the thermophysical quantities. The techniques of Fourier and Laplace transformations are used to present the problem exact solutions in the transformed domain by the eigenvalue approach. The inversions of the Fourier-Laplace transforms hold analytical and numerically. The numerical outcomes for the fiber-reinforced material are presented and graphically depicted. A comparison of the results for different theories under the fractional time derivative is presented. The properties of the fiber-reinforced material with the fractional derivative act to reduce the magnitudes of the variables considered, which can be significant in some practical applications and can be easily considered and accurately evaluated.

scholarly journals The Effect of Fractional Time Derivative of Bioheat Model in Skin Tissue Induced to Laser Irradiation

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 602
Author(s):  
Aatef Hobiny ◽  
Faris Alzahrani ◽  
Ibrahim Abbas ◽  
Marin Marin
Keyword(s):  
Laser Irradiation ◽  
Fractional Order ◽  
Time Derivative ◽  
Thermal Relaxation ◽  
Skin Tissue ◽  
Laplace Domain ◽  
Denatured Protein ◽  
Design Variables ◽  
New Interpretation ◽  
Fractional Time Derivative

This work uses the “fractional order bio-heat model” (Fob) model of heat conduction to offer a new interpretation to study the thermal damages in a skin tissue caused by laser irradiation. The influences of fractional order and the thermal relaxation time parameters on the temperature of skin tissue and the resulting thermal damage are studied. In the Laplace domain, the analytical solutions of temperature are obtained. Using the equation of Arrhenius, the resulting thermal injury to the tissues is assessed by the denatured protein ranges. The numerical results of the thermal damages and temperature are presented graphically. A parametric analysis is dedicated to the identifications of suitable procedures for the selection of significant design variables to achieve an effective thermal in the therapy of hyperthermia.

scholarly journals Rotation, Initial Stress, Gravity and Electromagnetic Field Effect on P Wave Reflection from Stress-Free Surface Elastic Half-Space with Voids under Three Thermoelastic Models

2020 ◽  
Vol 22 (1) ◽  
pp. 313-328 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
S. Z. Rida ◽  
R. A. Mohamed ◽  
A. A. Kilany
Keyword(s):  
Free Surface ◽  
Gravity Field ◽  
Initial Stress ◽  
Complex Modulus ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
P Wave ◽  
Reflection Coefficients

AbstractThe present paper is devoted to investigate the influence of the rotation, thermal field, initial stress, gravity field, electromagnetic and voids on the reflection of P wave under three models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), Lord-Shulman model (LS), Green-Lindsay model (GL), The boundary conditions at stress-free thermally insulated surface are satisfied to obtain Algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P1, P2, P3 and P4. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, initial stress, gravity field magnetic field, thermal relaxation times and voids parameters.

scholarly journals Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Majid Bagheri ◽  
Ali Khani
Keyword(s):  
Fractional Derivative ◽  
Exact Solutions ◽  
Fractional Order ◽  
Kdv Equation ◽  
Time Derivative ◽  
Hyperbolic Function ◽  
Nonlinear Phenomena ◽  
Generalized Kdv Equation ◽  
Wave Solutions ◽  
Fractional Time Derivative

The present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order α . Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional derivative which is used to get many solitary wave solutions by changing various parameters. The obtained solutions include three classes of soliton wave solutions in terms of hyperbolic function, trigonometric function, and rational function solutions. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of nonlinearity. Some of the nonlinear equations arise in fluid dynamics and nonlinear phenomena.

scholarly journals The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 207
Author(s):  
Tareq Saeed ◽  
Ibrahim A. Abbas
Keyword(s):  
Time Derivative ◽  
Wave Model ◽  
Physical Field ◽  
Thermoelastic Wave ◽  
Physical Fields ◽  
Transport Diffusion ◽  
Fractional Time Derivative ◽  
Without Energy Dissipation ◽  
Physical Quantities ◽  
Made In

In the present article, the generalized thermoelastic wave model with and without energy dissipation under fractional time derivative is used to study the physical field in porous two-dimensional media. By applying the Fourier-Laplace transforms and eigenvalues scheme, the physical quantities are presented analytically. The surface is shocked by heating (pulsed heat flow problem) and application of free traction on its outer surface (mechanical conditions) by the process of temperature transport (diffusion) to observe the full analytical solutions of the main physical fields. The magnesium (Mg) material is used to make the simulations and obtain numerical outcomes. The basic physical field quantities are graphed and discussed. Comparisons are made in the results obtained under the strong (SC), the weak (WC) and the normal (NC) conductivities.

Effects of Thermomechanical Coupling and Relaxation Times on Wave Spectrum in Dynamic Theory of Generalized Thermoelasticity

1998 ◽  
Vol 65 (3) ◽  
pp. 605-613 ◽  
Author(s):  
C. S. Suh ◽  
C. P. Burger
Keyword(s):  
Relaxation Time ◽  
Wave Spectrum ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
Thermomechanical Coupling ◽  
Order Of Magnitude ◽  
Relaxation Time Constants ◽  
Thermoelastic Waves ◽  
Insight Into

A spectral study is performed to gain insight into the effects of relaxation times and thermomechanical coupling on dynamic thermoe Iastic responses in generalized thermoelasticity. The hyperbolic thermoelastic theories of Lord and Schulman (LS) and Green and Lindsay (GL) are selected for the study. A generalized characteristic equation is derived to investigate dispersion behavior of thermoelastic waves as functions of thermomechanical coupling and relaxation time constants. Thermomechanical coupling is found to impose a significant influence on phase velocities. The GL model implicitly indicates that the order of magnitude of the thermomechanical relaxation time can never be greater than that of thermal relaxation time.

GENERALIZED FRACTIONAL ORDER BLOCH EQUATION WITH EXTENDED DELAY

2012 ◽  
Vol 22 (04) ◽  
pp. 1250071 ◽  
Author(s):  
SACHIN BHALEKAR ◽  
VARSHA DAFTARDAR-GEJJI ◽  
DUMITRU BALEANU ◽  
RICHARD MAGIN
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Time Derivative ◽  
Bloch Equation ◽  
Extended Model ◽  
Order Ordinary Differential Equation ◽  
Stability Behavior ◽  
System Memory ◽  
The Stability ◽  
Fractional Time Derivative

The fundamental description of relaxation (T1 and T2) in nuclear magnetic resonance (NMR) is provided by the Bloch equation, an integer-order ordinary differential equation that interrelates precession of magnetization with time- and space-dependent relaxation. In this paper, we propose a fractional order Bloch equation that includes an extended model of time delays. The fractional time derivative embeds in the Bloch equation a fading power law form of system memory while the time delay averages the present value of magnetization with an earlier one. The analysis shows different patterns in the stability behavior for T1 and T2 relaxation. The T1 decay is stable for the range of delays tested (1 μsec to 200 μsec), while the T2 relaxation in this extended model exhibits a critical delay (typically 100 μsec to 200 μsec) above which the system is unstable. Delays arise in NMR in both the system model and in the signal excitation and detection processes. Therefore, by adding extended time delay to the fractional derivative model for the Bloch equation, we believe that we can develop a more appropriate model for NMR resonance and relaxation.

Reflection of plane waves from a thermo-microstretch elastic solid with temperature dependent elastic properties

2014 ◽  
Vol 10 (2) ◽  
pp. 228-249 ◽  
Author(s):  
Ya Qin Song ◽  
Mohamed I.A. Othman ◽  
Zheng Zhao
Keyword(s):  
Reflection Coefficient ◽  
Harmonic Wave ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Angle Of Incidence ◽  
Temperature Dependent ◽  
Content Type

Purpose – The purpose of this paper is to study the reflection of a plane harmonic wave at the interface of thermo-microstretch elastic half space. The modulus of elasticity is taken as a linear function of reference temperature. The formulation is applied to generalized thermoelasticity theories, the Lord-Shulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. Using potential function, the governing equations reduce to ten-order differential equation. Design/methodology/approach – Coefficient ratios of reflection of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection with the angle of incidence is illustrated graphically for magnesium crystal micropolar material under three theories. Findings – The effect of different temperature-dependent constants and frequency on the coefficient ratios of reflection is illustrated graphically in context of Lord-Shulman theory. Originality/value – The reflection coefficient ratios are given analytically and illustrated graphically. The effects of thermal relaxation times are very small on reflection coefficient ratio. The temperature-dependent constant and wave frequency have a strong effect on the reflection coefficient ratios.

scholarly journals The Effects of Fractional Time Derivatives in Porothermoelastic Materials Using Finite Element Method

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1606
Author(s):  
Marin Marin ◽  
Aatef Hobiny ◽  
Ibrahim Abbas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Derivative ◽  
Thermal Relaxation ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Future Studies ◽  
Fractional Time Derivative ◽  
Insight Into ◽  
Element Method

In this work, a new model for porothermoelastic waves under a fractional time derivative and two time delays is utilized to study temperature increments, stress and the displacement components of the solid and fluid phases in porothermoelastic media. The governing equations are presented under Lord–Shulman theory with thermal relaxation time. The finite element method has been adopted to solve these equations due to the complex formulations of this problem. The effects of fractional parameter and porosity in porothermoelastic media have been studied. The numerical outcomes for the temperatures, the stresses and the displacement of the fluid and the solid are presented graphically. These results will allow future studies to gain a detailed insight into non-simple porothermoelasticity with various phases.

Sign in / Sign up

Export Citation Format

Share Document