scholarly journals Closed-Form Solutions of the Cross-Anisotropic Stratum Due to a Point Heat Source

10.5772/10023 ◽  
2010 ◽  
Author(s):  
Feng-Tsai Lin ◽  
John C.-C.
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Point Heat Source ◽  
Closed Form Solutions ◽  
The Cross

Point Heat Source Induced Thermoelastic Responses of the Cross-Anisotropic Strata

2014 ◽  
Vol 638-640 ◽  
pp. 517-529
Author(s):  
John C.C. Lu ◽  
Ming Qi Chen ◽  
Feng Tsai Lin
Keyword(s):  
Thermal Properties ◽  
Heat Source ◽  
Thermal Stresses ◽  
Fourier Transforms ◽  
Great Depth ◽  
Analytic Solutions ◽  
Mechanical And Thermal Properties ◽  
Point Heat Source ◽  
Closed Form Solutions ◽  
The Cross

This work presents the closed-form solutions of the long-term thermal stresses, displacements and temperature increment of the cross-anisotropic strata subjected to a point heat source at great depth. The medium is initially modeled with cross-anisotropic mechanical and thermal properties. Under this assumption, the properties of the materials are different between the planes on and normal to the isotropic plane. Using Hankel and Fourier transforms, this paper presents the analytic solutions to soils or rocks affected by the point heat source, such as the repositories of nuclear wastes. The general solutions are further simplified to cases of materials with isotropic mechanical properties, and they are finally extended to fully isotropic in each property of the strata. Based on numerical results, the thermal stresses, displacements and temperature change of the thermoelastic half space are significantly affected by the anisotropy of mechanical and thermal properties of the strata.

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.

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.

Melting Solid Plug Between Two Coaxial Pipes by a Moving Heat Source in the Inner Pipe

1994 ◽  
Vol 116 (4) ◽  
pp. 1028-1033 ◽  
Author(s):  
S. A. Fomin ◽  
P. S. Wei ◽  
V. A. Chugunov
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Surrounding Medium ◽  
Scale Analysis ◽  
Moving Heat Source ◽  
Closed Form Solutions ◽  
Entire Process ◽  
Annular Gap ◽  
Independent Parameters ◽  
Molten Region

Melting of a solid plug in the gap between two coaxial pipes by inserting a moving heat source in the inner pipe is investigated. Using a scale analysis, closed-form solutions for temperatures of liquid in the inner pipe, solid plug and liquid in the annular gap, and the surrounding medium around the outer pipe are determined. It is shown that eight independent dimensionless parameters are required to specify the entire process. The effects of independent parameters on the shapes of the molten region in the gap are found. The analysis and results provided are useful for the design of oil pipes.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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