Journal ArticleDOI
An integral equation approach to diffusion
TLDR
In this article, a method of solution of transient diffusion, e.g. heat conduction, problems in homogeneous and isotropic media with internal sources and arbitrary (including nonlinear) boundary conditions and initial conditions is proposed.About:
This article is published in International Journal of Heat and Mass Transfer.The article was published on 1974-06-01. It has received 86 citations till now. The article focuses on the topics: Integral equation & Electric-field integral equation.read more
Citations
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Journal ArticleDOI
Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method
TL;DR: In this paper, the Green's function for three-dimensional transient heat conduction (diffusion equation) for functionally graded materials (FGMs) is derived, and a Laplace transform (LT) approach is used to eliminate the dependence on time.
Book
The green element method
TL;DR: An element-by-element approach of implementing the Boundary Element Method (BEM) which offers substantial savings in computing resource, enables handling of a wider range of problems including non-linear ones, and at the same time preserves the second-order accuracy associated with the method.
Journal ArticleDOI
Application of the boundary element method to transient heat conduction
Gary F. Dargush,P. K. Banerjee +1 more
TL;DR: In this article, an advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components, which includes higher-order conforming elements, self-adaptive integration and a multiregion capability.
Journal ArticleDOI
Unsteady flow in confined aquifers: A comparison of two boundary integral methods
TL;DR: The boundary integral equation method (BIEM) is used for the solution of unsteady flow in confined aquifers as mentioned in this paper, where flows are described by a diffusion equation.
Journal ArticleDOI
Boundary integral equation solution of moving boundary phase change problems
TL;DR: In this article, a general formulation based on space-time Green's functions is developed using the complete heat equation, followed by a simpler formulation using the Laplace equation, and the latter is pursued and applied in detail.
References
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Book
Conduction of Heat in Solids
H. S. Carslaw,John Conrad Jaeger +1 more
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
Journal ArticleDOI
Numerical Solution of Ordinary and Partial Differential Equations
Journal ArticleDOI
A method of solution for certain problems of transient heat conduction
Frank J. Rizzo,D. J. Shippy +1 more
TL;DR: In this paper, an exact integral formula defined on the boundary of an arbitrary body is obtained from a fundamental singular solu- tion to the governing differential equation, such that the Laplace transformed temperature field may subsequently be generated by a Green's type integral identity.
Journal ArticleDOI
Nonlinear Heat Transfer Problem
TL;DR: In this paper, the time-dependent surface temperature of a body receiving heat according to the Stefan Boltzmann law has been investigated in a semi-infinite medium subject to a boundary condition which can involve the temperature in a nonlinear manner.