Small time approximations of Green's functions for one-dimensional heat conduction problems with convective boundaries

2003 ◽  
Vol 83 (8) ◽  
pp. 549-558 ◽  
Author(s):  
D.H.Y. Yen ◽  
J.V. Beck
Keyword(s):  
Heat Conduction ◽  
Green's Functions ◽  
Green’S Functions ◽  
Small Time ◽  
One Dimensional ◽  
Convective Boundaries

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 ANALITYCAL SOLUTION OF THE ONE DIMENSIONAL NONLINEAR TRANSIENT HEAT CONDUCTION PROBLEM USING GREEN’S FUNCTIONS

2021 ◽  
Vol 20 (2) ◽  
pp. 55
Author(s):  
S. S. Ribeiro ◽  
G. C. Oliveira ◽  
J. R. F. Oliveira ◽  
G. Guimarães
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Green's Functions ◽  
Green’S Functions ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
One Dimensional ◽  
Transient Heat Conduction Problem ◽  
Kirchhoff Transformation ◽  
Nonlinear Transient

Analytical solutions showed to be an important and strong tool for understand thermal problems using mathematic tools. In this work we propose an approach about one dimensional analytical solution for a nonlinear transient heat conduction problem, were used mathematical elements such as Kirchhoff transformation, Green’s functions and the combination of them.  The combination of this two methods showed that was possible to determinate an analytical solution for the nonlinear thermal problem, and showed a good approximation when compared with results from numerical methods.

scholarly journals Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

2019 ◽  
Vol 24 (1) ◽  
pp. 26 ◽  
Author(s):  
Sergey Davydov ◽  
Andrei Zemskov ◽  
Elena Akhmetova
Keyword(s):  
Half Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Local Equilibrium ◽  
Linear Equations ◽  
Integral Form ◽  
External Effects ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
The Laplace Transform

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes.

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