Heat Conduction with Local Heat Sources

2018 ◽  
pp. 325-350
Author(s):  
Sadık Kakaç ◽  
Yaman Yener ◽  
Carolina P. Naveira-Cotta
Keyword(s):  
Heat Conduction ◽  
Local Heat ◽  
Heat Sources

Heat Conduction With Local Heat Sources

2018 ◽  
pp. 289-312
Author(s):  
Yaman Yener ◽  
Sadık Kakaç
Keyword(s):  
Heat Conduction ◽  
Local Heat ◽  
Heat Sources

Heat Conduction in Composites: Homogenization and Macroscopic Behavior

1997 ◽  
Vol 50 (6) ◽  
pp. 327-356 ◽  
Author(s):  
Piotr Furman˜ski
Keyword(s):  
Heat Conduction ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Local Heat ◽  
Temperature Fields ◽  
Heat Sources ◽  
Ensemble Averaging ◽  
Macroscopic Behavior ◽  
Classical Behavior ◽  
Homogeneous Media

The review article discusses methods of macroscopic averaging of heat conduction in composite materials that lead to models of homogenized, macroscopic behavior of these media. It is shown that essentially two continuum models are in use: 1) the effective medium and 2) the mixture. The ensemble averaging technique allows one to derive the constitutive relations for both models assuming Fourier-like conduction on the microstructure level of a composite. These constitutive relations contain effective, macroscopic properties of the composite material which can be forecast when properties of individual constituents, the form of thermal interaction at constituent interfaces, amount of each material and its distribution are known. For weakly varying mean temperature fields, thermal behavior of the composite is essentially the same as homogeneous media but, for stronger variation, a non-classical behavior is observed. This non-classical behavior can be associated either with space nonlocality and memory phenomena or with wall effects and, in some cases, with influence of local heat sources on the effective properties. Most of these effects are not well known and need further detailed studies. The article includes 158 references.

Hyperbolic heat conduction due to axisymmetric continuous or pulsed surface heat sources

1990 ◽  
Vol 68 (11) ◽  
pp. 5478-5485 ◽  
Author(s):  
W. S. Kim ◽  
L. G. Hector ◽  
M. N. Özisik
Keyword(s):  
Heat Conduction ◽  
Surface Heat ◽  
Hyperbolic Heat Conduction ◽  
Heat Sources

scholarly journals A method for solving a boundary value problem in a multilayered area

2020 ◽  
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Boundary Value ◽  
Internal Heat ◽  
Electrical Machine ◽  
Problem Solution ◽  
Conductive Heat ◽  
Heat Sources ◽  
Internal Layers ◽  
Internal Heat Sources

A mathematical model of thermal process in an electrical machine was built as an example, presented as a three-layer cylinder where internal heat sources operate in one of the layers and heat is submitted to the other two by means of heat conduction. A method of solving the boundary-value problems for heat conduction equation in a complex area – a multi-layered cylinder with internal heat sources operating in one part of the layers and external ones in another part, is proposed. A method of problem solution in conditions of uncertainty of one of the boundary condition at the layers interface with conductive heat exchange between the layers is reviewed. The principle of method lies in the averaging of temperature distributions radially in the internal layers. As a result of transformations at the layers interface a boundary condition of the impedance-type conjugation appears. The analytical and numeric-analytical solutions of simplified problems were obtained.

scholarly journals Construction and investigation of new numerical algorithms for the heat equation : Part 2

2020 ◽  
Vol 10 (4) ◽  
pp. 339-348
Author(s):  
Mahmoud Saleh ◽  
Ádám Nagy ◽  
Endre Kovács
Keyword(s):  
Heat Conduction ◽  
Numerical Methods ◽  
Heat Conduction Equation ◽  
Space Dimension ◽  
Numerical Test ◽  
Numerical Algorithms ◽  
Heat Conducting ◽  
Heat Sources ◽  
Test Results ◽  
New Algorithms

This paper is the second part of a paper-series in which we create and examine new numerical methods for solving the heat conduction equation. Now we present numerical test results of the new algorithms which have been constructed using the known, but non-conventional UPFD and odd-even hopscotch methods in Part 1. Here all studied systems have one space dimension and the physical properties of the heat conducting media are uniform. We also examine different possibilities of treating heat sources.

scholarly journals 1-D heat conduction in a fractal medium: A solution by the local fractional Fourier series method

2013 ◽  
Vol 17 (3) ◽  
pp. 953-956 ◽  
Author(s):  
Yuzhu Zhang ◽  
Aimin Yang ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Series Method ◽  
Heat Transfer Mechanism ◽  
Basic Properties ◽  
Fractal Medium ◽  
Fourier Series Method

In this communication 1-D heat conduction in a fractal medium is solved by the local fractional Fourier series method. The solution developed allows relating the basic properties of the fractal medium to the local heat transfer mechanism.

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