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.

Fractional order generalized thermoelastic response in a half space due to a periodically varying heat source

2018 ◽  
Vol 14 (1) ◽  
pp. 2-15 ◽  
Author(s):  
Jitesh Tripathi ◽  
Shrikant Warbhe ◽  
K.C. Deshmukh ◽  
Jyoti Verma
Keyword(s):  
Mathematical Model ◽  
Heat Source ◽  
Laplace Transform ◽  
Half Space ◽  
Fractional Order ◽  
Order Parameter ◽  
Order Theory ◽  
Numerical Inversion ◽  
Content Type ◽  
Copper Material

Purpose The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues. Design/methodology/approach Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates. Findings This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter. Research limitations/implications Constructed purely on theoretical mathematical model by considering different parameters and the functions. Practical implications The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations. Originality/value In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

scholarly journals Effect of Variable Properties and Moving Heat Source on Magnetothermoelastic Problem under Fractional Order Thermoelasticity

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Chunbao Xiong ◽  
Ying Guo
Keyword(s):  
Heat Source ◽  
Fractional Order ◽  
Axial Direction ◽  
Moving Heat Source ◽  
Variable Properties ◽  
Governing Equations ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Temperature Dependent Properties ◽  
Nondimensional Temperature

A one-dimensional generalized magnetothermoelastic problem of a thermoelastic rod with finite length is investigated in the context of the fractional order thermoelasticity. The rod with variable properties, which are temperature-dependent, is fixed at both ends and placed in an initial magnetic field, and the rod is subjected to a moving heat source along the axial direction. The governing equations of the problem in the fractional order thermoelasticity are formulated and solved by means of Laplace transform in tandem with its numerical inversion. The distributions of the nondimensional temperature, displacement, and stress in the rod are obtained and illustrated graphically. The effects of the temperature-dependent properties, the velocity of the moving heat source, the fractional order parameter, and so forth on the considered variables are concerned and discussed in detail, and the results show that they significantly influence the variations of the considered variables.

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.

scholarly journals Sandwich structure panel subjected to thermal loading using fractional order equation of motion and moving heat source

2018 ◽  
Vol 96 (2) ◽  
pp. 174-182 ◽  
Author(s):  
E. Bassiouny ◽  
Hamdy M. Youssef
Keyword(s):  
Heat Source ◽  
Laplace Transform ◽  
Fractional Order ◽  
Sandwich Structure ◽  
Thermal Loading ◽  
Present Model ◽  
Generalized Thermoelasticity ◽  
Equation Of Motion ◽  
Order Equation ◽  
Moving Heat Source

The present work studies the thermoelastic behaviour of a model for a layered thin plate called sandwich structure subjected to a thermal shock wave in light of the generalized thermoelasticity theory using fractional order equation of motion in the presence of a moving heat source. The governing equations are solved using Laplace transform. To obtain the different inverse field functions numerically, we used a complex inversion formula of Laplace transform based on Fourier expansion. The effect of different parameters; namely, the speed, the strength of the heat source, fractional order and time on the thermodynamical temperature, stress, and strain distribution, are discussed and presented graphically. Comparison with previous work in the context of the theory of generalized thermoelasticity shows that the present model is more reliable than the previous. The present model removes the points of discontinuity present in the stress and temperature distributions in the previous model. In the present model we found that the middle layer was affected slightly by some of these parameters. The other new results are discussed.

Generalized Thermoelastic Responses of a Piezoelectric Rod Subjected to a Moving Heat Source

2007 ◽  
Vol 353-358 ◽  
pp. 1149-1152
Author(s):  
Tian Hu He ◽  
Li Cao
Keyword(s):  
Numerical Calculation ◽  
Heat Source ◽  
Laplace Transformation ◽  
Moving Heat Source ◽  
Governing Equations ◽  
Laplace Inversion ◽  
Thermally Induced ◽  
Numerical Laplace Inversion ◽  
Generalized Thermoelastic ◽  
Elastic Responses

Based on the Lord and Shulman generalized thermo-elastic theory, the dynamic thermal and elastic responses of a piezoelectric rod fixed at both ends and subjected to a moving heat source are investigated. The generalized piezoelectric-thermoelastic coupled governing equations are formulated. By means of Laplace transformation and numerical Laplace inversion the governing equations are solved. Numerical calculation for stress, displacement and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed.

Thermoelastic Interactions in a Slim Strip Due to a Moving Heat Source Under Dual-Phase-Lag Heat Transfer

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Nantu Sarkar ◽  
Sudip Mondal
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Laplace Transform ◽  
Time Domain ◽  
Generalized Thermoelasticity ◽  
Inverse Laplace Transform ◽  
Phase Lag ◽  
Dual Phase ◽  
Moving Heat Source ◽  
Transient Phenomena

Abstract Following the link of work of He and Cao (2009, Math. Comput. Modell., 49(7–8), 1719–1720), we employ the theory of generalized thermoelasticity with dual-phase-lag (DPL) to study the transient phenomena in a thin slim strip due to a moving heat source. Both ends of the strip are assumed to be fixed and thermally insulated. Using Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the strip are carried out and presented graphically. The effect of moving heat source speed on temperature, stress, and displacement is studied. The temperature, displacement, and stress in the strip are found to be decreasing at large source speed.

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