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

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.

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

Journal of Tribology ◽

10.1115/1.2920699 ◽

1991 ◽

Vol 113 (4) ◽

pp. 828-831 ◽

Cited By ~ 2

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.

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A unified approach to closed-form solutions of moving heat-source problems

Heat and Mass Transfer ◽

10.1007/s002310050209 ◽

1998 ◽

Vol 33 (5-6) ◽

pp. 415-424 ◽

Cited By ~ 9

Author(s):

S. M. Zubair ◽

M. Aslam Chaudhry

Keyword(s):

Heat Source ◽

Closed Form ◽

Moving Heat Source ◽

Unified Approach ◽

Closed Form Solutions

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Analysis of hyperbolic Pennes bioheat equation in perfused homogeneous biological tissue subject to the instantaneous moving heat source

SN Applied Sciences ◽

10.1007/s42452-021-04379-w ◽

2021 ◽

Vol 3 (4) ◽

Author(s):

Ali Kabiri ◽

Mohammad Reza Talaee

Keyword(s):

Heat Source ◽

Closed Form ◽

Method Comparison ◽

Closed Form Solution ◽

Form Solution ◽

Temperature Profiles ◽

Moving Heat Source ◽

Bioheat Equation ◽

Perfusion Rate

AbstractThe one-dimensional hyperbolic Pennes bioheat equation under instantaneous moving heat source is solved analytically based on the Eigenvalue method. Comparison with results of in vivo experiments performed earlier by other authors shows the excellent prediction of the presented closed-form solution. We present three examples for calculating the Arrhenius equation to predict the tissue thermal damage analysis with our solution, i.e., characteristics of skin, liver, and kidney are modeled by using their thermophysical properties. Furthermore, the effects of moving velocity and perfusion rate on temperature profiles and thermal tissue damage are investigated. Results illustrate that the perfusion rate plays the cooling role in the heating source moving path. Also, increasing the moving velocity leads to a decrease in absorbed heat and temperature profiles. The closed-form analytical solution could be applied to verify the numerical heating model and optimize surgery planning parameters.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.638-640.2082 ◽

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.

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Temperature Field Due to a Moving Heat Source: A Moving Mesh Finite Element Analysis

Journal of Applied Mechanics ◽

10.1115/1.3169040 ◽

1985 ◽

Vol 52 (2) ◽

pp. 274-280 ◽

Cited By ~ 45

Author(s):

Z.-B. Kuang ◽

S. N. Atluri

Keyword(s):

Finite Element ◽

Temperature Field ◽

Heat Source ◽

Process Zone ◽

Surrounding Medium ◽

Moving Mesh ◽

Transient Temperature ◽

Moving Heat Source ◽

Element Analysis ◽

External Agent

The transient temperature field (as seen by a moving observer) due to a moving heat source, such as the process zone near a dynamically propagating crack tip or an external agent as in the case of welding, is analyzed by a moving-mesh finite element procedure. The effects of the temperature-dependent material properties, and of the loss of heat to the surrounding medium through convection and radiation, are studied. Situations under which conditions in the process zone may be labeled as “isothermal” or “adiabatic” are explored. Estimates of temperature rise near the tip of a crack propagating at realistic speeds in structural steels are made.

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