Identification of heat transfer mathematical models based on non-contact measurements


Аuthors

Nenarokomov A. V.1*, Semenov D. S.2**, Dombrovsky L. A.3

1. ,
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
3. ,

*e-mail: nenarokomovav@mai.ru
**e-mail: semenov_ds@icloud.com

Abstract

Mathematical model application adequate enough to the real heat transfer process in biological tissues is necessary to solve the problem of individual thermal protection structure optimization. Indirect measurements, usually leading to the necessity of solving the inverse heat exchange problems, are the only way to solve this problem. The paper considers one-dimensional problem of an opaque material periodic heating by the pulsed laser irradiation in the presence of convective heat exchange with an external medium on the surface of a material. Property package definition of a heat insulating material in conditions of non-stationary heating based on the reverse heat exchange problem solution is the purpose of research. The considered system is an unlimited opaque flat plate affected on its left border by the laser heat flux, acting orthogonal to a surface. Heat exchange with external medium takes place both on the left and right borders. The article proposes a modified algorithm for inverse problem solving on determining characteristics of thermal exchange on the surface, accounting for a priori information on the fact that the characteristics being determined are constant. As additional information necessary for mathematical model identification at the unknown thermo-physical characteristics, non-contact temperature measurements on the sample surface are employed. Method of iterative regularization is one of the most versatile methods of the ill-posed inverse heat exchange problems. From the computation general sequence viewpoint, such iteration algorithms are built according to the traditional optimization procedure based on the gradient methods. As applied to the problem numerical solution the following procedure is applied: the initial approximation of the unknown characteristic is set (zero, or based on a priori information); then the direct boundary problem and a system of problems for the temperature increment were being solved; the unknown characteristics increment and the value of the minimized functional are being computed, and the condition of iterative process completion is checked. The presented work studied the process of impulse heating of an opaque material by laser. The temperature measurements herewith were performed in conditions when contact temperature measuring sensors application was not possible, including thermocouples on the sample surface, which is peculiar to the porous materials. The authors formulated a mathematical model, describing the non-stationary process of an opaque sample heating. A program for the heat transfer coefficient and a laser thermal flux restoring was developed. Approbation of the method under development by the computational experiment was performed applying the developed software. In addition, the temperature measurement sensor error was modeled and its impact on the problem solution was studied.

Keywords:

mathematical models identification, inverse heat transfer problem, radiation-conductive heat transfer, non-contact temperature measurements

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