Two-temperature generalized thermoelasticity with fractional order strain of an infinite body with a spherical cavity

2018 ◽  
Vol 18 (4) ◽  
pp. 1055-1066 ◽  
Author(s):  
Eman A. N. Al-Lehaibi
Keyword(s):  
Fractional Order ◽  
Spherical Cavity ◽  
Generalized Thermoelasticity ◽  
Infinite Body ◽  
Two Temperature

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 The Fractional Strain Influence on a Solid Sphere under Hyperbolic Two-Temperature Generalized Thermoelasticity Theory by Using Diagonalization Method

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hamdy M. Youssef ◽  
Alaa A. El-Bary ◽  
Eman A. N. Al-Lehaibi
Keyword(s):  
Fractional Order ◽  
Radial Distance ◽  
Generalized Thermoelasticity ◽  
Solid Sphere ◽  
Temperature Function ◽  
Thermoelasticity Theory ◽  
Mechanical Waves ◽  
Diagonalization Method ◽  
Temperature Parameter ◽  
Two Temperature

This article constructs a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere. In the context of the hyperbolic two-temperature generalized thermoelasticity theory, the governing equations have been established. Thermally and without deformation, the sphere’s bounding surface is shocked. The singularities of the functions examined at the center of the world were decreased by using L’Hopital’s rule. Numerical results with different parameter fractional-order values, the double temperature function, radial distance, and time have been graphically illustrated. The two-temperature parameter, radial distance, and time have significant effects on all the studied functions, and the fractional-order parameter influences only mechanical functions. In the hyperbolic two-temperature theory as well as in one-temperature theory (the Lord-Shulman model), thermal and mechanical waves spread at low speeds in the thermoelastic organization.

scholarly journals Two-Temperature Generalized Thermoviscoelasticity with Fractional Order Strain Subjected to Moving Heat Source: State Space Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Renu Yadav ◽  
Kapil Kumar Kalkal ◽  
Sunita Deswal
Keyword(s):  
Heat Source ◽  
State Space ◽  
Fractional Order ◽  
Mechanical Load ◽  
Generalized Thermoelasticity ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Conductive Temperature ◽  
Special Cases ◽  
Two Temperature

The theory of generalized thermoelasticity with fractional order strain is employed to study the problem of one-dimensional disturbances in a viscoelastic solid in the presence of a moving internal heat source and subjected to a mechanical load. The problem is in the context of Green-Naghdi theory of thermoelasticity with energy dissipation. Laplace transform and state space techniques are used to obtain the general solution for a set of boundary conditions. To tackle the expression of heat source, Fourier transform is also employed. The expressions for different field parameters such as displacement, stress, thermodynamical temperature, and conductive temperature in the physical domain are derived by the application of numerical inversion technique. The effects of fractional order strain, two-temperature parameter, viscosity, and velocity of internal heat source on the field variables are depicted graphically for copper material. Some special cases of interest have also been presented.

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.

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