Transient heat conduction in a medium with two circular cavities: Semi-analytical solution

Elizaveta Gordeliy; Steven L. Crouch; Sofia G. Mogilevskaya

doi:10.1016/j.ijheatmasstransfer.2007.10.021

Transient heat conduction in a medium with two circular cavities: Semi-analytical solution

Elizaveta Gordeliy, Steven L. Crouch, Sofia G. Mogilevskaya

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Abstract

This paper considers a transient heat conduction problem for an infinite medium with two non-overlapping circular cavities. Suddenly applied, steady Dirichlet type boundary conditions are assumed. The approach is based on superposition and the use of the general solution to the problem of a single cavity. Application of the Laplace transform results in a semi-analytical solution for the temperature in the form of a truncated Fourier series. The large-time asymptotic formulae for the solution are obtained by using the analytical solution in the Laplace domain. The method can be extended to problems with multiple cavities and inhomogeneities.

Original language	English (US)
Pages (from-to)	3556-3570
Number of pages	15
Journal	International Journal of Heat and Mass Transfer
Volume	51
Issue number	13-14
DOIs	https://doi.org/10.1016/j.ijheatmasstransfer.2007.10.021
State	Published - Jul 1 2008

Keywords

Addition theorem
Asymptotic series
Fourier series
Laplace transform
Modified Helmholtz equation
Transient heat conduction

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title = "Transient heat conduction in a medium with two circular cavities: Semi-analytical solution",

abstract = "This paper considers a transient heat conduction problem for an infinite medium with two non-overlapping circular cavities. Suddenly applied, steady Dirichlet type boundary conditions are assumed. The approach is based on superposition and the use of the general solution to the problem of a single cavity. Application of the Laplace transform results in a semi-analytical solution for the temperature in the form of a truncated Fourier series. The large-time asymptotic formulae for the solution are obtained by using the analytical solution in the Laplace domain. The method can be extended to problems with multiple cavities and inhomogeneities.",

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author = "Elizaveta Gordeliy and Crouch, {Steven L.} and Mogilevskaya, {Sofia G.}",

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T2 - Semi-analytical solution

AU - Gordeliy, Elizaveta

AU - Crouch, Steven L.

AU - Mogilevskaya, Sofia G.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - This paper considers a transient heat conduction problem for an infinite medium with two non-overlapping circular cavities. Suddenly applied, steady Dirichlet type boundary conditions are assumed. The approach is based on superposition and the use of the general solution to the problem of a single cavity. Application of the Laplace transform results in a semi-analytical solution for the temperature in the form of a truncated Fourier series. The large-time asymptotic formulae for the solution are obtained by using the analytical solution in the Laplace domain. The method can be extended to problems with multiple cavities and inhomogeneities.

AB - This paper considers a transient heat conduction problem for an infinite medium with two non-overlapping circular cavities. Suddenly applied, steady Dirichlet type boundary conditions are assumed. The approach is based on superposition and the use of the general solution to the problem of a single cavity. Application of the Laplace transform results in a semi-analytical solution for the temperature in the form of a truncated Fourier series. The large-time asymptotic formulae for the solution are obtained by using the analytical solution in the Laplace domain. The method can be extended to problems with multiple cavities and inhomogeneities.

KW - Addition theorem

KW - Asymptotic series

KW - Fourier series

KW - Laplace transform

KW - Modified Helmholtz equation

KW - Transient heat conduction

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JO - International Journal of Heat and Mass Transfer

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ER -

Transient heat conduction in a medium with two circular cavities: Semi-analytical solution

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