scholarly journals Fractional Order Two-Temperature Dual-Phase-Lag Thermoelasticity with Variable Thermal Conductivity

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Sudip Mondal ◽  
Sadek Hossain Mallik ◽  
M. Kanoria
Keyword(s):  
Thermal Conductivity ◽  
Fractional Order ◽  
Generalized Thermoelasticity ◽  
Variable Thermal Conductivity ◽  
Fourier Series Expansion ◽  
Phase Lag ◽  
Dual Phase ◽  
The Laplace Transform ◽  
Matrix Differential ◽  
Two Temperature

A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by using a state space approach. The inversion of Laplace transforms is computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, temperature discrepancy, and the fractional order parameter.

Fractional Order Two Temperature Generalized Thermoelasticity in a Symmetric Spherical Shell

2020 ◽  
Vol 8 (1) ◽  
pp. 91-104
Author(s):  
Mohsin Islam ◽  
Keyword(s):  
Spherical Shell ◽  
Fractional Order ◽  
Outer Boundary ◽  
Generalized Thermoelasticity ◽  
Fourier Series Expansion ◽  
Phase Lag ◽  
Conductive Temperature ◽  
The Laplace Transform ◽  
Matrix Differential ◽  
Two Temperature

This paper deals with the determination of thermoelastic stresses, strain and conductive temperature in a spherically symmetric spherical shell in the context of the fractional order two temperature generalized thermoelasticity theory (2TT). The two temperature three-phase-lag thermoelastic model (2T3P) and two temperature Green Naghdi model III (2TGN-III) are combined into a unified formulation. There is no temperature at the outer boundary and thermal load is applied at the inner boundary. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace- transform domain which is then solved by the state-space approach. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The physical quantities have been computed numerically and presented graphically. The effect of the fractional order parameter on the solutions has been studied and the comparisons among different thermoelastic models are made.

scholarly journals Characterization of the Vibration and Strain Energy Density of a Nanobeam under Two-Temperature Generalized Thermoelasticity with Fractional-Order Strain Theory

2021 ◽  
Vol 26 (4) ◽  
pp. 78
Author(s):  
Hamzah Abdulrahman Alharthi
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Generalized Thermoelasticity ◽  
Strain Theory ◽  
Aspect Ratios ◽  
The Laplace Transform ◽  
Beam Thickness ◽  
Novel Model ◽  
Two Temperature

In this work, fractional-order strain theory was applied to construct a novel model that introduces a thermal analysis of a thermoelastic, isotropic, and homogeneous nanobeam. Under supported conditions of fixed aspect ratios, a two-temperature generalized thermoelasticity theory based on one relaxation time was used. The governing differential equations were solved using the Laplace transform, and their inversions were found by applying the Tzou technique. The numerical solutions and results for a thermoelastic rectangular silicon nitride nanobeam were validated and supported in the case of ramp-type heating. Graphs were used to present the numerical results. The two-temperature model parameter, beam size, ramp-type heat, and beam thickness all have a substantial influence on all of the investigated functions. Moreover, the parameter of the ramp-type heat might be beneficial for controlling the damping of nanobeam energy.

scholarly journals Thermoelastic Interactions in a Rotating Infinite Orthotropic Elastic Body with a Cylindrical Hole and Variable Thermal Conductivity

2017 ◽  
Vol 64 (4) ◽  
pp. 481-498 ◽  
Author(s):  
D. S. Mashat ◽  
A. M. Zenkour ◽  
A. E. Abouelregal
Keyword(s):  
Thermal Conductivity ◽  
Hoop Stress ◽  
Generalized Thermoelasticity ◽  
Variable Thermal Conductivity ◽  
Cylinder Surface ◽  
Laplace Transform Technique ◽  
Rotation Phase ◽  
The Laplace Transform ◽  
Phase Lags ◽  
Effects Of Rotation

Abstract In the present article, we introduced a new model of the equations of generalized thermoelasticity for unbounded orthotropic body containing a cylindrical cavity. We applied this model in the context of generalized thermoelasticity with phase-lags under the effect of rotation. In this case, the thermal conductivity of the material is considered to be variable. In addition, the cylinder surface is traction free and subjected to a uniform unit step temperature. Using the Laplace transform technique, the distributions of the temperature, displacement, radial stress and hoop stress are determined. A detailed analysis of the effects of rotation, phase-lags and the variability thermal conductivity parameters on the studied fields is discussed. Numerical results for the studied fields are illustrated graphically in the presence and absence of rotation.

scholarly journals The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Hamdy M. Youssef ◽  
Najat A. Alghamdi
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Constant Heat Flux ◽  
Bioheat Transfer ◽  
Skin Tissue ◽  
Phase Lag ◽  
Dual Phase ◽  
Constant Heat ◽  
Two Temperature

Abstract This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

scholarly journals Magnetic field on surface waves propagation in gravitational thermoelastic media with two temperature and initial stress in the context of three theories

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 285-299
Author(s):  
Jamel Bouslimi ◽  
Sayed Abo-Dahab ◽  
Khaled Lotfy ◽  
Sayed Abdel-Khalek ◽  
Eied Khalil ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Initial Stress ◽  
Half Space ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Mathematical Methods ◽  
Numerical Work ◽  
Suitable Material ◽  
Two Temperature

In this paper is investigating the theory of generalized thermoelasticity under two temperature is used to solve boundary value problems of 2-D half-space its bound?ary with different types of heating under gravity effect. The governing equations are solved using new mathematical methods under the context of Lord-Shulman, Green-Naghdi theory of type III (G-N III) and the three-phase-lag model to inves?tigate the surface waves in an isotropic elastic medium subjected to gravity field, magnetic field, and initial stress. The general solution obtained is applied to a spe?cific problem of a half-space and the interaction with each other under the influence of gravity. The physical domain by using the harmonic vibrations is used to obtain the exact expressions for the Waves velocity and attenuation coefficients for Stoneley waves, Love waves, and Rayleigh waves. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The results obtained are calculated numerical?ly and presented graphically with some comparisons in the absence and the presence the influence of gravity, initial stress and magnetic field. It clears that the results ob?tained agree with the physical practical results and agree with the previous results if the gravity, two temperature, and initial stress neglect as special case from this study.

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