A new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids

A new simple analytical method for solving the problem of one-dimensional transient heat conduction in a slab of finite thickness is proposed, in which the initial temperature is assumed zero or constant and the boundary surfaces are assumed to be at constant temperature, constant heat flux, or insu...

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Autores principales:	Sumio KATO, Shoichi MATSUDA
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2017
Materias:	heat conduction analytical method one-dimensional transient heat conduction initial-boundary value problem semi-infinite solid slab Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/b3860c3435684e0599d000281b498e1f
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spelling	oai:doaj.org-article:b3860c3435684e0599d000281b498e1f2021-11-26T07:03:57ZA new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids2187-974510.1299/mej.17-00096https://doaj.org/article/b3860c3435684e0599d000281b498e1f2017-06-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/4/3/4_17-00096/_pdf/-char/enhttps://doaj.org/toc/2187-9745A new simple analytical method for solving the problem of one-dimensional transient heat conduction in a slab of finite thickness is proposed, in which the initial temperature is assumed zero or constant and the boundary surfaces are assumed to be at constant temperature, constant heat flux, or insulated. In this method, the solution is expressed by an infinite series representation, each term of which is the temperature solution of the corresponding initial-boundary value problem for the semi-infinite solid. Each semi-infinite solid extends to infinity in the positive or negative direction of the x axis and the surface is located at various positions along the x axis. Each term and the partial sum in the infinite series automatically satisfy the heat conduction equation and the initial condition. The solution is easily constructed so that the boundary values of the partial sum converge to those of the heat conduction problem as the number of terms N increases to infinity. The basic concept of the solution method for the problem of one-dimensional transient heat conduction in a slab is described. The solution method is applied to various initial-boundary value problems. The formulas of the typical solutions by this method are found to be the same as those of the solutions obtained by other literature using the method of Laplace transformation, which supports the validity of the new solution method proposed in this paper. The usefulness of this method is also examined.Sumio KATOShoichi MATSUDAThe Japan Society of Mechanical Engineersarticleheat conductionanalytical methodone-dimensional transient heat conductioninitial-boundary value problemsemi-infinite solidslabMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 4, Iss 3, Pp 17-00096-17-00096 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	heat conduction analytical method one-dimensional transient heat conduction initial-boundary value problem semi-infinite solid slab Mechanical engineering and machinery TJ1-1570
spellingShingle	heat conduction analytical method one-dimensional transient heat conduction initial-boundary value problem semi-infinite solid slab Mechanical engineering and machinery TJ1-1570 Sumio KATO Shoichi MATSUDA A new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids
description	A new simple analytical method for solving the problem of one-dimensional transient heat conduction in a slab of finite thickness is proposed, in which the initial temperature is assumed zero or constant and the boundary surfaces are assumed to be at constant temperature, constant heat flux, or insulated. In this method, the solution is expressed by an infinite series representation, each term of which is the temperature solution of the corresponding initial-boundary value problem for the semi-infinite solid. Each semi-infinite solid extends to infinity in the positive or negative direction of the x axis and the surface is located at various positions along the x axis. Each term and the partial sum in the infinite series automatically satisfy the heat conduction equation and the initial condition. The solution is easily constructed so that the boundary values of the partial sum converge to those of the heat conduction problem as the number of terms N increases to infinity. The basic concept of the solution method for the problem of one-dimensional transient heat conduction in a slab is described. The solution method is applied to various initial-boundary value problems. The formulas of the typical solutions by this method are found to be the same as those of the solutions obtained by other literature using the method of Laplace transformation, which supports the validity of the new solution method proposed in this paper. The usefulness of this method is also examined.
format	article
author	Sumio KATO Shoichi MATSUDA
author_facet	Sumio KATO Shoichi MATSUDA
author_sort	Sumio KATO
title	A new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids
title_short	A new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids
title_full	A new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids
title_fullStr	A new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids
title_full_unstemmed	A new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids
title_sort	new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids
publisher	The Japan Society of Mechanical Engineers
publishDate	2017
url	https://doaj.org/article/b3860c3435684e0599d000281b498e1f
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A new analytical method for solving the problem of one-dimensional transient heat conduction in a slab by using the temperature solutions of semi-infinite solids

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