Abstract
The aim of this paper is to present two techniques for simply and accurately determining space-variable heat transfer coefficient, given measurements of temperature at some interior points in the body. The fluid temperature is also measured as part of the solution. The methods are formulated as linear and non-linear least-squares problems. The unknown parameters associated with the solution of the inverse heat conduction problem (IHCP) are selected to achieve the closest agreement in a least squares sense between the computed and measured temperatures using the Levenberg–Marquardt method (method I) or the singular value decomposition (method II). The methods presented in the paper are used for determining the local heat transfer coefficient on the circumference of the vertical smooth tube placed in the tube bundle with a staggered tube arrangement. Good agreement between the results is obtained. The uncertainties in the estimated heat transfer coefficients are calculated using the error propagation rule of Gauss. The main advantage of the presented methods is that they do not require any complex simulation of flow and temperature field in the fluid.
Zusammenfassung
In der Arbeit wurden zwei Verfahren zur einfachen und genauen Bestimmung des lokalen Wärmeübergangskoeffizienten auf der Basis der in inneren Punkten des Körpers gemessenen Temperaturen entwickelt. Die Umgebungstemperatur wird auch gemessen. Das erste Verfahren wird als lineare und das zweite Verfahren als nichtlineare Aufgabe der kleinsten Quadrate formuliert. Die unbekannten Parameter, die in dem inversen Problem der Wärmeleitung auftreten, werden so gewählt, daß die beste Übereinstimmung zwischen den berechneten und gemessenen Temperaturen erzielt wird. Zur Bestimmung der unbekannten Parameter wurden zwei Methoden angewandt: das Verfahren von Levenberg–Marquardt (Methode I) und die singuläre Matrix-Zerlegung (Methode II). Die entwickelten Methoden wurden zur Bestimmung des örtlichen Wärmeübergangskoeffizienten an der außen Oberfläche des Rohres, das sich in der Bündel mit der versetzten Rohranordnung befindet, angewandt. Die Unsicherheiten in den ermittelten Wärmeübergangskoeffizienten wurden nach dem Gaußschen Prinzip der Fehler Fortpflanzung berechnet. Eine numerische Simulation des Temperatur- und Strömungsfeldes im Fluidgebiet ist nicht notwendig, was der Hauptvorteil der beiden Methoden ist.
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Taler, J. Determination of local heat transfer coefficient from the solution of the inverse heat conduction problem . Forsch Ingenieurwes 71, 69–78 (2007). https://doi.org/10.1007/s10010-006-0044-2
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DOI: https://doi.org/10.1007/s10010-006-0044-2