Thermo-elastic stresses in a half-space having an isolated heat source on the boundary

1963 ◽  
Vol 14 (2) ◽  
pp. 160-166
Author(s):  
John T. Holden
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Elastic Stresses

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.

Steady-State Motion of a Line Mechanical/Heat Source Over a Half-Space: A Thermoelastodynamic Solution

1997 ◽  
Vol 64 (3) ◽  
pp. 562-567 ◽  
Author(s):  
L. M. Brock ◽  
H. G. Georgiadis
Keyword(s):  
Steady State ◽  
Heat Source ◽  
Half Space ◽  
Constant Velocity ◽  
Characteristic Length ◽  
Surface Displacement ◽  
Contact Problems ◽  
Governing Equations ◽  
Asymptotic Expressions ◽  
Thermoelastic Characteristic

An asymptotic solution within the bounds of steady-state coupled thermoelastodynamic theory is given for the surface displacement and temperature due to a line mechanical/heat source that moves at a constant velocity over the surface of a half-space. This problem is of basic interest in the fields of contact mechanics and tribology, and an exact formulation is considered. The results may serve as a Green’s function for more general thermoelastodynamic contact problems. The problem may also be viewed as a generalization of the classical Cole-Huth problem and the associated Georgiadis-Barber correction. Asymptotic expressions are obtained by means of the two-sided Laplace transform, and by performing the inversions exactly. The range of validity of these expressions is actually quite broad, because of the small value of the thermoelastic characteristic length appearing in the governing equations.

Closed-Form Solutions of the Elastic Half Space due to a Line Heat Source

2014 ◽  
Vol 638-640 ◽  
pp. 2082-2091
Author(s):  
John C.C. Lu ◽  
Feng Tsai Lin
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Line Heat Source ◽  
Closed Form Solutions ◽  
Line Sink ◽  
Vertical Displacements ◽  
Thermoelastic Response

Thermoelastic response due to a line heat source is analog to poroelastic reaction caused by a fluid line sink. In this study, the strata are modeled as a thermoelastic or poroelastic half space bounded by horizontal surface in the mathematical model. Thermomechanics and poromechanics are applied on the formulation of basic governing equations, and an analogy is drawn to show the similarity. Using Hankel transform technique and approaching symbolic integral through Mathematica, the closed-form solutions of the horizontal and vertical displacements due to a fluid line sink are obtained. The displacements produced by the line heat source are described through analog quantities between thermoelasticity and poroelasticity. The solutions can be applied to dewater operations and build waste repository.

Thermoelastic Solutions for Thermal Distributions Moving Over Half Space Surfaces and Application to the Moving Heat Source

1988 ◽  
Vol 55 (1) ◽  
pp. 87-92 ◽  
Author(s):  
M. D. Bryant
Keyword(s):  
Fourier Transform ◽  
Heat Source ◽  
Half Space ◽  
Elastic Half Space ◽  
Temperature Wave ◽  
Exact Results ◽  
Moving Heat Source ◽  
Exponential Fourier Transform

A method is developed for obtaining fundamental thermal and thermoelastic solutions for thermal distributions moving over the surface of an elastic half space. This method uses the concept of a moving temperature wave along with a novel form of an exponential Fourier transform. The technique is developed and then demonstrated on the example of a moving heat source. Exact results are matched with results from Carslaw and Jaeger (1959) and Barber (1984).

scholarly journals Two-Dimensional Deformation in a Thermoelastic Solid with Microtemperatures Subjected to an Internal Heat Source

2018 ◽  
Vol 23 (1) ◽  
pp. 5-21 ◽  
Author(s):  
P. Ailawalia ◽  
S. Budhiraja ◽  
J. Singh
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Normal Mode Analysis ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Thermoelastic Medium ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid

AbstractThe purpose of this paper is to study the two dimensional deformation in a generalized thermoelastic medium with microtemperatures having an internal heat source subjected to a mechanical force. The force is acting along the interface of generalized thermoelastic half space and generalized thermoelastic half space with microtemperatures having an internal heat source. The normal mode analysis has been applied to obtain the exact expressions for the considered variables. The effect of internal heat source and microtemperatures on the above components has been depicted graphically.

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