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.

Elastic Solutions for a Saturated Isotropic Half Space Subjected to a Fluid Line Sink

2013 ◽  
Vol 405-408 ◽  
pp. 275-284 ◽  
Author(s):  
John C.C. Lu
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Mass Conservation ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Governing Equations ◽  
Closed Form Solutions ◽  
Cylindrical Coordinate ◽  
Line Sink ◽  
The Mathematical Model

The study derives the closed-form solutions of the long-term elastic consolidation subjected to the fluid line sink in a homogeneous isotropic elastic half space aquifer. The Hankel transform in a cylindrical coordinate system is employed to develop the analytical elastic solutions. Derivations of governing equations are based on the mathematical model of Biots theory of poro-mechanics, and the half space aquifer is modelled as a saturated porous stratum which is bounded by a horizontal surface. The total stresses of the aquifer obey Newtons second law and Hookes law. Besides, the mass conservation and Darcys law are introduced to formulate the governing equations of pore fluid flow. The software Mathematica is used to complete the symbolic integrations and obtain the closed-form solutions. The solutions can be applied in dewatering operations of compressible aquifer.

Closed-Form Expression for Temperature in a Semi-Infinite Solid Due to a Fast Moving Surface Heat Source

1991 ◽  
Vol 113 (4) ◽  
pp. 828-831 ◽  
Author(s):  
J. A. Tichy
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Frictional Contact ◽  
Closed Form Expression ◽  
Moving Heat Source ◽  
Convolution Integral ◽  
Form Expression ◽  
Exponential Integral ◽  
Surface Conditions ◽  
Closed Form Solutions

In the thermal analysis of an asperity on a sliding surface in frictional contact with an opposing surface, conditions are often idealized as a moving heat source. The solution to this problem at arbitrary Pe´cle´t number in terms of a singular integral is well known. In this study, closed-form solutions are found in terms of the exponential integral for high Pe´cle´t number. Fortunately, the closed-form solutions are accurate at Pe´cle´t number of order one. While several restrictions are necessary, the closed-form expressions offer considerable numerical savings relative to evaluations of the convolution integral.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

Analysis of wave propagation in the presence of a continuous line heat source under heat transfer with memory dependent derivatives

2017 ◽  
Vol 23 (5) ◽  
pp. 820-834 ◽  
Author(s):  
Rakhi Tiwari ◽  
Santwana Mukhopadhyay
Keyword(s):  
Heat Transfer ◽  
Wave Propagation ◽  
Time Delay ◽  
Heat Source ◽  
Hankel Transform ◽  
Heat Transfer Process ◽  
Numerical Results ◽  
Continuous Line ◽  
Line Heat Source ◽  
With Memory

In the present work, the recently proposed new concept of “memory dependent derivative” in heat transfer process in a solid body has been employed to investigate the problem of wave propagation in a homogeneous, isotropic and unbounded solid due to a continuous line heat source. Both Laplace and Hankel transform techniques are employed for the solution of the problem. Analytical results for the distributions of different fields like temperature, displacement and stresses inside the medium have been derived. The problem is illustrated by computing the numerical values of the field variables for a particular material. We have attempted to exhibit the significance of a kernel function and a time-delay parameter that are characteristic of memory dependent derivative heat transfer in the behavior of field variables such as temperature, displacement and stresses with the help of numerical results. Detailed comparative analysis is represented through the numerical results to estimate the effects of the kernels and time-delay parameter on the behavior of all of the field variables such as temperature, displacement and stresses in the presence of a heat source in the medium.

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).

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