scholarly journals Connection between heat diffusion and heat conduction in one-dimensional systems

2013 ◽  
Vol 56 (8) ◽  
pp. 1466-1471 ◽  
Author(s):  
ShunDa Chen ◽  
Yong Zhang ◽  
Jiao Wang ◽  
Hong Zhao
Keyword(s):  
Heat Conduction ◽  
Heat Diffusion ◽  
One Dimensional

scholarly journals Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions

2016 ◽  
Vol 2016 ◽  
pp. 1-22
Author(s):  
Inês Simões ◽  
António Tadeu ◽  
Nuno Simões
Keyword(s):  
Heat Conduction ◽  
Frequency Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Heat Diffusion ◽  
One Dimensional ◽  
The Time Domain ◽  
Point Line

This paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane heat diffusion sources. Particular attention is given to the case of spatially sinusoidal, harmonic line sources. In the literature this problem is often referred to as the two-and-a-half-dimensionalfundamental solutionor 2.5D Green’s functions. These equations are very useful for formulating three-dimensional thermodynamic problems by means of integral transforms methods and/or boundary elements. The image source technique is used to build up different geometries such as half-spaces, corners, rectangular pipes, and parallelepiped boxes. The final expressions are verified here by applying the equations to problems for which the solution is known analytically in the time domain.

scholarly journals On the semi-inverse method and variational principle

2013 ◽  
Vol 17 (5) ◽  
pp. 1565-1568 ◽  
Author(s):  
Xue-Wei Li ◽  
Ya Li ◽  
Ji-Huan He
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Inverse Method ◽  
Generalized Variational Principle ◽  
Open Forum ◽  
One Dimensional ◽  
History Of

In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.?s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.

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