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.

Thermodynamic behaviour of microstretch viscoelastic solids with internal heat source

2014 ◽  
Vol 92 (5) ◽  
pp. 425-434 ◽  
Author(s):  
Sunita Deswal ◽  
Renu Yadav
Keyword(s):  
Heat Source ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Moving Heat Source ◽  
Line Heat Source ◽  
Epoxy Material ◽  
Mech Phys Solid

The dynamical interactions caused by a line heat source moving inside a homogeneous isotropic thermo-microstretch viscoelastic half space, whose surface is subjected to a thermal load, are investigated. The formulation is in the context of generalized thermoelasticity theories proposed by Lord and Shulman (J. Mech. Phys. Solid, 15, 299 (1967)) and Green and Lindsay (Thermoelasticity, J. Elasticity, 2, 1 (1972)). The surface is assumed to be traction free. The solutions in terms of displacement components, mechanical stresses, temperature, couple stress, and microstress distribution are procured by employing the normal mode analysis. The numerical estimates of the considered variables are obtained for an aluminium–epoxy material. The results obtained are demonstrated graphically to show the effect of moving heat source and viscosity on the displacement, stresses, and temperature distribution.

A Two-Dimensional Problem for a Rotating Magneto-Thermoelastic Half-Space with Voids and Gravity in a Two-Temperature Generalized Thermoelasticity Theory

2015 ◽  
Vol 31 (6) ◽  
pp. 639-651 ◽  
Author(s):  
S. Deswal ◽  
N. Hooda
Keyword(s):  
Half Space ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Hyperbolic Heat Conduction ◽  
Conduction Model ◽  
Conductive Temperature ◽  
Two Temperature

ABSTRACTThe present paper is concerned with an in-depth study of the effects of rotation, two-temperature parameter and voids on the magneto-thermoelastic interactions in a homogeneous, isotropic, generalized half-space with gravity field. The formulation is applied within the frame-work of two-temperature generalized thermoelasticity based on the hyperbolic heat conduction model with one relaxation time. Using normal mode analysis technique for the physical variables appearing in the governing equations, we get the analytical expressions for displacement components, stress, thermodynamic temperature, conductive temperature and change in volume fraction field. The general solution obtained is then applied to a specific problem of an infinite half-space having isothermal boundary subjected to mechanical load. Variations of the considered variables through the vertical distance are illustrated graphically.

Unsteady Temperature Distribution in a Sphere Subjected to Time-Dependent Surface Heat Flux and Internal Heat Source

1969 ◽  
Vol 91 (1) ◽  
pp. 45-50 ◽  
Author(s):  
N. Y. O¨lc¸er
Keyword(s):  
Heat Flux ◽  
Temperature Distribution ◽  
Heat Source ◽  
Surface Heat Flux ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Surface Heat ◽  
Initial Temperature Distribution ◽  
Unsteady Temperature ◽  
Special Cases

General expressions are derived for the three-dimensional unsteady heating of a solid sphere under the influence of a variable internal heat source and an arbitrary initial temperature distribution when the entire surface is subjected to a variable heat flux. Both the volume heat source and the surface heat flux are prescribed in terms of arbitrary functions of space and time. Various forms of solutions are noted. These expressions, not available hitherto, contain the solutions of many special problems of technological importance. The results presented in two recent studies on the arbitrary heating of spheres are shown to be special cases of the general sphere problem treated here and the errors appearing in these studies are corrected. Other special cases are also discussed.

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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