Application of fractional order theory of thermoelasticity to a 1D problem for a half-space

2013 ◽  
Vol 94 (6) ◽  
pp. 509-515 ◽  
Author(s):  
H.H. Sherief ◽  
A.M. Abd El-Latief
Keyword(s):  
Half Space ◽  
Fractional Order ◽  
Order Theory

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.

Interactions due to hall current and rotation in a magneto-micropolar fractional order thermoelastic half-space subjected to ramp-type heating

2016 ◽  
Vol 12 (1) ◽  
pp. 133-150 ◽  
Author(s):  
Rajneesh Kumar ◽  
Kulwinder Singh ◽  
Devinder Pathania
Keyword(s):  
Half Space ◽  
Fractional Order ◽  
Hall Current ◽  
Order Theory ◽  
Order Derivative ◽  
Field Equations ◽  
Content Type ◽  
Fractional Order Derivative ◽  
Coupled Field Equations ◽  
Thermoelastic Solid

Purpose – The purpose of this paper is to investigate a two dimensional problem in magneto-micropolar thermoelastic half-space with fractional order derivative in the presence of combined effects of hall current and rotation subjected to ramp-type heating. Design/methodology/approach – The fractional order theory of thermoelasticity with one relaxation time derived by Sherief et al. (2010) has been used to investigate the problem. Laplace and Fourier transform technique has been used to solve the resulting non-dimensional coupled field equations to obtain displacement, stress components and temperature distribution. A numerical inversion technique has been applied to obtain the solution in the physical domain. Findings – Numerical computed results of all the considered variables have been shown graphically to depict the combined effect of hall current and rotation. Some particular cases of interest are also deduced from the present study. Originality/value – Comparison are made in the presence and absence of hall current and rotation in a magneto-micropolar thermoelastic solid with fractional order derivative.

scholarly journals The Effect of Magnetic Field and Initial Stress on Fractional Order Generalized Thermoelastic Half-Space

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sunita Deswal ◽  
Sandeep Singh Sheoran ◽  
Kapil Kumar Kalkal
Keyword(s):  
Magnetic Field ◽  
Initial Stress ◽  
Half Space ◽  
Fractional Order ◽  
Generalized Thermoelasticity ◽  
Order Theory ◽  
Homogeneous Half Space ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Space Formulation

The aim of this paper is to study magneto-thermoelastic interactions in an initially stressed isotropic homogeneous half-space in the context of fractional order theory of generalized thermoelasticity. State space formulation with the Laplace transform technique is used to obtain the general solution, and the resulting formulation is applied to the ramp type increase in thermal load and zero stress. Solutions of the problem in the physical domain are obtained by using a numerical method of the Laplace inverse transform based on the Fourier expansion technique, and the expressions for the displacement, temperature, and stress inside the half-space are obtained. Numerical computations are carried out for a particular material for illustrating the results. Results obtained for the field variables are displayed graphically. Some comparisons have been shown in figures to present the effect of fractional parameter, ramp parameter, magnetic field, and initial stress on the field variables. Some particular cases of special interest have been deduced from the present investigation.

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