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The purpose of this paper is to present the method for solving the inverse Cauchy-type problem for the Laplace’s equation. Calculations were made for the rectangular domain with the target temperature on three boundaries and, additionally, on one of the boundaries, the heat flux distribution was selected. The purpose of consideration was to determine the distribution of temperature on a section of the boundary of the investigated domain (boundary Γ₁) and find proper method for the problem regularization.

The solution of the direct and the inverse (Cauchy-type) problems for the Laplace’s equation is presented in the paper. The form of the solution is noted as the linear combination of the Chebyshev polynomials. The collocation method in which collocation points had been determined based on the Chebyshev nodes was applied. To solve the Cauchy problem, the minimum of functional describing differences between the target and the calculated values of temperature and the heat flux on a section of the domain’s boundary was sought. Various types of the inverse problem regularization, based on Tikhonov and Tikhonov–Philips regularizations, were analysed. Regularization parameter α was chosen with the use of the Morozov discrepancy principle.

Calculations were performed for random disturbances to the heat flux density of up to 0.01, 0.02 and 0.05 of the target value. The quality of obtained results was next estimated by means of the norm. Effect of the disturbance to the heat flux density and the type of regularization on the sought temperature distribution on the boundary Γ₁ was investigated. Presented methods of regularization are considerably less sensitive to disturbances to measurement data than to Tikhonov regularization.

Discussed in this paper is an example of solution of the Cauchy problem for the Laplace’s equation in the rectangular domain that can be applied for determination of the temperature distribution on the boundary of the heated element where it is impossible to measure temperature or the measurement is subject to a great error, for instance on the inner wall of the boiler. Authors investigated numerical examples for functions with singularities outside the domain, for which values of gradients change significantly within the calculation domain what corresponds to significant changes in temperature on the wall of the boiler during the fuel combustion.

In this paper, a new method for solving the Cauchy problem for the Laplace’s equation is described. To solve this problem, the Chebyshev polynomials and nodes were used. Various types of regularization of this problem were considered.

To reduce the heat load of a gas turbine blade, its surface is covered with an outer layer of ceramics with high thermal resistance. The purpose of this paper is the selection of ceramics with such a low heat conduction coefficient and thickness, so that the permissible metal temperature is not exceeded on the metal-ceramics interface due to the loss ofmechanical properties.

Therefore, for given temperature changes over time on the metal-ceramics interface, temperature changes over time on the inner side of the blade and the assumed initial temperature, the temperature change over time on the outer surface of the ceramics should be determined. The problem presented in this way is a Cauchy type problem. When analyzing the problem, it is taken into account that thermophysical properties of metal and ceramics may depend on temperature. Due to the thin layer of ceramics in relation to the wall thickness, the problem is considered in the area in the flat layer. Thus, a one-dimensional non-stationary heat flow is considered.

The range of stability of the Cauchy problem as a function of time step, thickness of ceramics and thermophysical properties of metal and ceramics are examined. The numerical computations also involved the influence of disturbances in the temperature on metal-ceramics interface on the solution to the inverse problem.

The computational model can be used to analyze the heat flow in gas turbine blades with thermal barrier.

A number of inverse problems of the type considered in the paper are presented in the literature. Inverse problems, especially those Cauchy-type, are ill-conditioned numerically, which means that a small change in the inputs may result in significant errors of the solution. In such a case, regularization of the inverse problem is needed. However, the Cauchy problem presented in the paper does not require regularization.

T-shaped cavities occur by design in many technical applications. An example of such a stator cavity is the side space between the guide vane carriers and the outer casing of a steam turbine. Thermal conditions inside it have a significant impact on the deformation of the turbine casing. In order to improve its prediction, the purpose of this paper is to provide a methodology to gain better knowledge of the local heat transfer at the cavity boundaries based on experimental results.

To determine the heat transfer coefficient distribution inside a model cavity with the help of a scaled generic test rig, an inverse heat conduction problem is posed and a method for solving such type of problems in the form of linear combinations of Trefftz functions is presented.

The results of the calculations are compared with another inverse method using first-order gradient optimization technique as well as with estimated values obtained with an analytic two-dimensional thermal network model, and they show an excellent agreement. The calculation procedure is proved to be numerically stable for different degrees of complexity of the sought boundary conditions.

This paper provides a universal and robust methodology for the fast direct determination of an arbitrary distribution of heat transfer coefficients based on material temperature measurements spread over the confining wall.

This paper aims to present the Cauchy problem for the Laplace’s equation for profiles of gas turbine blades with one and three cooling channels. The distribution of heat transfer coefficient and temperature on the outer boundary of the blade are known. On this basis, the temperature on inner surfaces of the blade (the walls of cooling channels) is determined.

Such posed inverse problem was solved using the finite element method in the domain of the discrete Fourier transform (DFT).

Calculations indicate that the regularization in the domain of the DFT enables obtaining a stable solution to the inverse problem. In the example under consideration, problems with reconstruction constant temperature, assumed on the outer boundary of the blade, in the vicinity of the trailing and leading edges occurred.

The application of DFT in connection with regularization is an original achievement presented in this study.

This paper aims to present the problem of heating the damaged insulation of an orbiter.

Changes of the insulation’s thermal properties, made by adding conductive material of high value of specific heat in a form of a dope to the protective layer, were examined. An iterative algorithm determining a variable of dope concentration in the material was developed.

Determination of distribution of conductive material concentration was made for materials which, after verification, demonstrated the most beneficial effect on protective properties of the modified insulation layer. The problem of determining the distribution of metal filings concentration in the insulation layer of the coating belongs to inverse heat conduction problems.

Change of properties was to enable time extension of the LI900 insulation tile heating up to the maximal temperature and, additionally, to lowering this temperature.

Aims to focus on steady state and transient state analysis of basic properties of new solution for a single‐phase serial AC voltage controller. Furthermore, simulation and experimental test results of 3 kVA models are provided to confirm and verify the theoretical approach.

Presents a converter with auxiliary transformer and bipolar PWM AC matrix‐reactance chopper (MRC), based on Ćuk B2 topology. The MRC has the possibility of bipolar AC voltage conversion with magnitude of voltage transformation function greater than 1. The peak voltage detection method in the control circuit is applied to fast control of the load voltage changes. The steady state and transient state theoretical analysis based on averaged models of the presented controller is used. There is a four‐terminal description of the basic properties in the presented approach.

In the proposed solution only half the number of switches compared with the case of full bridge matrix chopper solution is used. The nominal load voltage can be obtained even for 50 per cent step‐down of the supply voltage.

Presents new topology and properties of single‐phase serial AC voltage controller.

The purpose of this paper is to develop a capacitor fully integrated into a wearable textile fabric for the application on smart clothing.

A small capacitor with stainless steel yarns as the electrodes and poly-(3,4–ethylenedioxythiophene): polystryrene sulphonate (PEDOT:PSS) as the dielectric material has been made, integrated into a textile fabric. The electric performance of the capacitor was analyzed and compared with other kinds of electric capacitors.

The fabricated small, PEDOT:PSS capacitor could finally power a calculator for 37 s with the energy stored in it.

This finding is of an important significance for a further development on the capacitor with a better performance.

The purpose of this paper is to focus on the application of the Trefftz method to the calculation of the two-dimensional (2D) temperature field in the boiling refrigerant flow through an asymmetrically heated vertical minichannel with a rectangular cross-section. The considerations were limited to determining the temperature of the continuous phase – liquid for bubbly and bubbly-slug flow. The numerical solution found with the Trefftz methods was compared with the simplified solution. For nucleate boiling, heat transfer coefficient at the heating foil – liquid contact was determined.

The Trefftz method was used to determine 2D temperature distributions for the glass pane, the heating foil and the boiling liquid. The temperature fields were approximated by the sum of the particular solution and the linear combination of suitable Trefftz functions. Coefficients of linear combination were computed using experimental data, including heating foil temperature measurements obtained with the liquid-crystal method and experimentally determined void fraction. The computations were based on the Trefftz method supplemented with the adjustment calculus.

The way of solving direct and inverse problems of heat conduction in solid bodies (isolating glass, heating foil) and in liquids (boiling refrigerant flowing through the minichannel) was presented. For the first time, both 2D temperature fields for the heating foil and the boiling liquid were calculated while simultaneously using the Trefftz method. The known temperature values of the foil and liquid allowed the calculation of the heat transfer coefficient and the heat flux at the heating foil-liquid contact. Adjustment calculus implemented into the Trefftz method was used to smooth the measurement data and to reduce their errors.

The approach proposed in the paper can be applied to determining 2D temperature field, heat flux and heat transfer coefficient in direct and inverse problems concerning two-phase flowing miniature compact heat exchangers.

The paper presents a novel implementation of the Trefftz method to simultaneous solving an inverse problem in the heating foil and the contacting flowing liquid.