×

zbMATH — the first resource for mathematics

A modified method for determining the surface heat flux of IHCP. (English) Zbl 1202.80017
Summary: We consider the determination of the surface heat flux of a body from a measured temperature history at a fixed location inside the body. Mathematically, it is formulated as a problem for the one-dimensional heat equation in a quarter plane with data given along the line \(x = 1\), and the gradient of the solution is determined for \(0\leq x < 1\). This problem is of practical interest in some engineering contexts and it is severely ill-posed, in the sense that the solution (if it exists) does not depend continuously on the data. In this article, we employ a fourth-order modified method to solve the problem. Some stability estimates are given. Numerical examples show that the modified method works very well.

MSC:
80A23 Inverse problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
35R30 Inverse problems for PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Beck JV, Inverse Heat Conduction: Ill-posed Problems (1985)
[2] DOI: 10.1088/0266-5611/13/2/007 · Zbl 0871.35105 · doi:10.1088/0266-5611/13/2/007
[3] Cannon JR, The One-dimensional Heat Equation (1984)
[4] DOI: 10.1088/0266-5611/3/2/009 · Zbl 0645.35094 · doi:10.1088/0266-5611/3/2/009
[5] DOI: 10.1137/S1064827597331394 · Zbl 0959.65107 · doi:10.1137/S1064827597331394
[6] DOI: 10.1155/IJMMS.2005.393 · Zbl 1079.35101 · doi:10.1155/IJMMS.2005.393
[7] DOI: 10.1007/BF01773508 · Zbl 0544.35049 · doi:10.1007/BF01773508
[8] DOI: 10.1137/0142040 · Zbl 0498.35084 · doi:10.1137/0142040
[9] DOI: 10.1088/0266-5611/11/4/017 · Zbl 0839.35143 · doi:10.1088/0266-5611/11/4/017
[10] DOI: 10.1115/1.2824112 · doi:10.1115/1.2824112
[11] DOI: 10.1016/j.cam.2005.04.031 · Zbl 1093.65107 · doi:10.1016/j.cam.2005.04.031
[12] DOI: 10.1002/1097-0207(20010220)50:5<1253::AID-NME81>3.0.CO;2-6 · Zbl 1082.80003 · doi:10.1002/1097-0207(20010220)50:5<1253::AID-NME81>3.0.CO;2-6
[13] DOI: 10.1016/0017-9310(81)90144-7 · Zbl 0468.76086 · doi:10.1016/0017-9310(81)90144-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.