A Green's Function for the Domain Bounded by Nonconcentric Spheres

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Jeng-Tzong Chen ◽  
Jia-Wei Lee ◽  
Hung-Chih Shieh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Fundamental Solutions ◽  
Dirichlet Boundary Conditions ◽  
Method Of Fundamental Solutions ◽  
Circular Cylinders ◽  
Image Method ◽  
Eccentric Annulus ◽  
Function Solution ◽  
Good Agreement

The main result is the analytical derivation of Green's function for the domain bounded by nonconcentric spheres in terms of bispherical coordinates. Both surfaces, inner and outer boundaries, are specified by the Dirichlet boundary conditions. This work can be seen as an extension study for the Green's function of eccentric annulus derived by Heyda (1959, “A Green's Function Solution for the Case of Laminar Incompressible Flow Between Non-Concentric Circular Cylinders,” J. Franklin Inst., 267, pp. 25–34). To verify the solution, a semianalytical solution using the image method and a numerical solution using the method of fundamental solutions (MFS) are utilized for comparisons. Good agreement is made.

Green’s Function Solution of Dual-Phase-Lag Model

2009 ◽  
Author(s):  
Yung-Ming Lee ◽  
Pei-Chi Lin ◽  
Tsung-Wen Tsai
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Green’S Function ◽  
Green's Function ◽  
Phase Lag ◽  
Micro Scale ◽  
Function Solution ◽  
Lag Model ◽  
Temperature Solution ◽  
Good Agreement

In this study, the micro-scale heat conduction solution in a finite rigid slab computed with and without heat source is investigated. The analytical solution is derived by Laplace transform (LT) technique and Green’s function solution (GFS) method. The effect of heat source on the micro-scale heat conduction solution is also included in this paper. It is found that the temperature solution obtained by GFS method is smaller than that obtained by LT technique, and the GFS is in very good agreement with the solution obtained by the conventional Fourier’s law when τq = τT. Moreover, the temperature distributions computed by the LT technique are always overestimated in this study owing to the absence of the G2 effect. Hence, it is believed that the temperature solutions predicted by the GFS-LT method are more accurate than those evaluated by the LT technique. When time is increasing, the discrepancies of temperature solutions among various methods for τT > τq is increasing.

A Liouville Type Theorem for Poly-harmonic System with Dirichlet Boundary Conditions in a Half Space

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Zhao Liu ◽  
Wei Dai
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Dirichlet Boundary ◽  
Type Theorem ◽  
Dirichlet Boundary Conditions ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Harmonic System

AbstractIn this paper, we consider the following poly-harmonic system with Dirichlet boundary conditions in a half space ℝwherewhereis the Green’s function in ℝ

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