O. M. Alifanov

Solution of an inverse problem of heat conduction by iteration methods

An iteration scheme for determining nonstationary heat flux is constructed for the linear case. The scheme is based on the two gradient slope methods.

Regularized numerical solution of nonlinear inverse heat-conduction problem

The construction of an algorithm for a numerical solution of the nonlinear inverse problem is discussed for the case of a generalized one-dimensional heat-conduction equation in a region with moving boundaries. The algorithm is regularized in the Tikhonov manner.

Application of the regularization principle to the formulation of approximate solutions of inverse heat-conduction problems

The synthesis of a Tikhonov-regularizing algorithm is discussed for the solution of integral equations in inverse heat-conduction problems of the first kind.

Mathematical simulation of high-porosity fibrous materials and determination of their physical properties

A statistical mathematical model of fibrous high-porosity composite material is described. This model is used for studying the basic radiative and thermophysical properties of material. It is demonstrated how the use of the model helps significantly extend the capabilities of experimental methods and enables one to compare the calculation and experimental results and obtain parameters of material which were previously hardly accessible for determination.

Application of iterative regularization for the solution of incorrect inverse problems

The solution of inverse heat-conduction problems using regularizing gradient algorithms is considered.

Estimation of thermal properties of materials with application for inflatable spacecraft structure testing

The general method of iterative regularization is concerned with application to the estimation of material properties. The objective of this article is to estimate thermal and thermokinetic properties of advanced materials using the approach based on inverse methods. An experimental–computational system is presented for investigating the thermal and kinetics properties of composite materials by methods of inverse heat transfer problems and this is developed at the Thermal Laboratory of the Department of Space Systems Engineering, Moscow Aviation Institute. The system is aimed at investigating the materials in conditions of unsteady contact heating over a wide range of temperature changes and heating rates in vacuum, air and inert gas mediums.

A method of taking account ofa priori information in solving incorrect inverse problems

An approach to taking into accounta priori information about the smoothness of the function being restored is elucidated, as are also values of the function and its derivatives at a number of points of the domain of definition.

Inverse boundary-value problems of heat conduction

Possible formulations of the problems of determining heat fluxes and temperatures at the boundary of a solid from known temperatures within the solid are examined. A classification of these formulations is offered. Various methods for solving one-dimensional inverse problems are analyzed.

Estimating thermal and radiative properties of insulating materials

In many practical situations, it is impossible to measure directly the characteristics, such as thermal and radiative properties, of analysed materials. The only way which can often be used to overcome these difficulties is indirect measurements. This type of measurement is usually formulated as the solution of inverse heat transfer problems. The experimental methods of identification of the mathematical models of heat transfer based on solving the inverse problems are one of the modern effective solving manners. The main purpose of this article is to estimate thermal and radiative properties of advanced materials (thermal conductivity , heat capacity and emissivity ) using the approach based on inverse methods. New metrology under development is the combination of accurate enough measurements, which can be experimentally observable under real conditions, and accurate data processing, which are based on the solutions of inverse heat transfer problems. In this article, the development of methods for estimating thermal and radiation characteristics is carried out for thermally stable, high-temperature insulating materials. Such problems are of great practical importance in the study of properties of materials used as non-destructive surface coating in objects of space engineering, power engineering, etc.

Formulas for the discrepancy gradient in the iterative solution of inverse heat-conduction problems. II. Determining the gradient in terms of a conjugate variable

The construction of the functional-deficiency gradient is considered for the iterative solution of inverse problems in the case of an equation of parabolic type. Nonlinear formulations of the problem are considered in the general case.