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Abstract [en]
We consider a Cauchy problem for a parabolic equation as a mathematical model of the temperature development inside a suction pyrometer. Such devices are often used to calibrate the temperature sensor in a combustion chamber. Mathematically the problem is severely ill-posed and needs to be regularized. The model is simplified to make it one-dimensional in space. The temperature measurements are done in two steps. First, the heat transfer coefficient is approximated via a calibration experiment. Then the gas temperature in the combustion chamber is computed using a convection boundary condition. In both steps one computes the surface temperature and heat flux based on interior measurements in the thermocouple. Numerical examples are presented to test the proposed approach.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2010. p. 27
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2010:2
Keywords
Conduction, convective boundary condition, heat transfer coefficient, ill-posed, Volterra integral operator
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-54294 (URN)
2010-03-082010-03-082013-08-30Bibliographically approved