An integral solution for the inverse heat conduction problem after the method of Weber
type: Item
instance of: scholarly article
title: An integral solution for the inverse heat conduction problem after the method of Weber
zbMATH Open document ID: 0642.65079
DOI: 10.1016/0898-1221(88)90070-3
author: D. A. Murio
author: C. C. Roth
publication date: 1988-01-01T00:00:00Z
review text: The inverse heat conduction problem (IHCP) amounts to calculating, for a thermally conducting solid, the surface heat flux and/or temperature data from measured temperatures at an interior point. Generally, this is an ill-posed problem. Taking a one-dimensional semi-infinite slab as the body, the IHCP has the following mathematical formulation: The temperature \(u=u(x,t)\) satisfies \(\partial u/\partial t=\partial\) 2u/\(\partial x\) 2, \(0<x<\infty\), \(t>0\), \(u(x,0)=0\), \(0\leq x<\infty\), u(x,t) bounded as \(x\to \infty\), \(t>0\), \(u(1,t)=F(t)\), \(-u_ x(0,t)=q(t)\) for \(t>0\), with F measured, q unknown. Here t stands for time and x for the distance from the heated surface. The flux condition may be replaced by \(u(0,t)=f(t)\), \(t>0.\) This problem is handled through an algorithm based on an integral representation of Weber's hyperbolic approximation, using a filtered version of the noisy data. Error bounds are obtained and numerical experiments presented indicate the stability and accuracy of the method, as well as the proper choice of parameters.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 4047012
zbMATH Keywords: inverse heat conduction problem
zbMATH Keywords: ill-posed problem
zbMATH Keywords: algorithm
zbMATH Keywords: integral representation
zbMATH Keywords: Weber's hyperbolic approximation
zbMATH Keywords: noisy data
zbMATH Keywords: Error bounds
zbMATH Keywords: numerical experiments
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: 0898-1221(88)90070-3
OpenAlex ID: W2092190146
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published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 4047012