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The main purpose of this study, reflecting mainly the content of the authors’ plenary lecture, is to make a brief overview of several approaches developed by the author and his colleagues to the solution to ill-posed inverse heat transfer problems (IHTPs) with their possible extension to a wider class of inverse problems of mathematical physics and, most importantly, to show the wide possibilities of this methodology by examples of aerospace applications. In this regard, this study can be seen as a continuation of those applications that were discussed in the lecture.

The application of the inverse method was pre-tested with experimental investigations on a special test equipment in laboratory conditions. In these studies, the author used the solution to the nonlinear inverse problem in the conjugate (conductive and convective) statement. The corresponding iterative algorithm has been developed and tested by a numerical and experimental way.

It can be stated that the theory and methodology of solving IHTPs combined with experimental simulation of thermal conditions is an effective tool for various fundamental and applied research and development in the field of heat and mass transfer.

With the help of the developed methods of inverse problems, the investigation was conducted for a porous cooling with a gaseous coolant for heat protection of the re-entry vehicle in the natural environment of hypersonic flight. Moreover, the analysis showed that the inverse methods can make a useful contribution to the study of heat transfer at the surface of a solid body under the influence of the hypersonic heterogeneous (dusty) gas stream and in many other aerospace applications.

The purpose of this study is to optimize multilayer vacuum thermal insulation (MLI) of modern high-weight spacecrafts. An adequate mathematical simulation of heat transfer in the MLI is impossible if there is no available information on the main insulation properties.

The results of experiments in thermo-vacuum facilities are used to re-estimate some radiative properties of metallic foil/metalized polymer foil and spacer on the basis of the inverse problem solution. The experiments were carried out for the sample of real MLI used for the BP-Colombo satellite (ESA). The recently developed theoretical model based on neglecting possible near-field effects in radiative heat transfer between closely spaced aluminum foils was used in theoretical predictions of heat transfer through the MLI.

A comparison of the computational results and the experimental data confirms that there are no significant near-field effects between the neighboring MLI layers. It means that there is no considerable contradiction between the far-field model of radiative transfer in MLI and the experimental estimates.

An identification procedure for mathematical model of the multilayer thermal insulation showed that a modified theoretical model developed recently can be used to estimate thermal properties of the insulation at conditions of space vacuum.

The presented paper aims to consider algorithm for optimal design of multilayer thermal insulation.

Developed algorithm is based on a sequential quadratic programming method.

2D mathematical model of heat transfer in thermal protection was considered in frame of thermal design of spacecraft. The sensitivity functions were used to estimate the Jacobean of the object functions.

Design of distributed parameter systems and shape optimization may be thought of as geometrical inverse problems, in which the positions of free boundaries are determined along with the spatial variables. In such problems, the missing data (i.e. the position of boundaries) are compensated for by the presence of the so-called inverse problem additional conditions. In the case under consideration, such conditions are constrains on the temperature values at the discrete points of the system.

Results are presented how to apply the algorithm suggested for solving a practical problem – thickness sampling for a thermal protection system of advanced solar probe.

The procedure proposed in the paper to solve a design problem is based on the method of quadratic approximation of the initial problem statement as a Lagrange formulation. This has allowed to construct a rather universal algorithm applicable without modification for solving a wide range of thermal design problems.