Analytical Solution of Problems about the Radiative and Radiative–Conductive Stationary Heat Transfer in a Medium with an Arbitrary Dependence of the Scattering and Absorption on Frequency Boundary Conditions

We defined a method for the analytical solution of problems on stationary radiative and radiative–conductive heat transfer in a medium with an arbitrary frequency dependence of absorption and scattering near its boundary. We obtained formulas for the heat conductance of the remote surface and the thickness of the radiative–conductive relaxation of the medium. We determined characteristics of radiant heat transfer from the medium to free space such as the radiation spectrum, the radiation temperature and the medium outer boundary temperature. In addition, we solved the problem on the radiative–conductive heat transfer from one of two parallel surfaces to another with a medium between them.

Thermal insulation efficiency for underground structures in permafrost

In continuation of the previously published research results (Energy Safety and Energy Economy, iss. 1, 2021), the current study investigates thermal insulation efficiency for underground structures in permafrost conditions. Thermal insulation experiences the influence of various factors affecting its efficiency. For the purpose of this research, said efficiency was evaluated by intensity of heat flow from air to the ground. The non-stationary heat transfer coefficient, the so-called Kirpichev number, reflects for heat flow intensity. The 3D diagrams show the results of the study with a large data coverage for proper evaluation of thermal insulation efficiency of underground structures in permafrost. The results confirm that thermal insulation can be considered effective both for short-term and long-term underground workings.

Estimation of a Thermal Conductivity in a Stationary Heat Transfer Problem with a Solid-Solid Interface

An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, made up of two consecutive sections of different, isotropic and homogeneous materials, perfectly assembly, where one of the materials, that is unreachable and unknown, has to be identified. The length of the bar is assumed to be much greater that the diameter so that a 1D heat transfer process is considered. A constant temperature is assumed at the end of the unknown part of the rod while the other end is let free for convection. We propose a procedure to identify the unknown material of the bar based on a noisy flow measurement at the opposite end. Necessary and sufficient conditions are derived together with a bound for the estimation error. Moreover, elasticity analysis is performed to study the influence of the data in the conductivity estimation and numerical examples are included to illustrate the proposed ideas and show the estimation performance.

MATHEMATICAL MODELLING OF NON-STATIONARY HEAT TRANSFER IN A MULTILAYER COMPOSITE MATERIAL

The article considers the issue of designing a composite textile material based on the use of a 3D textile matrix for firefighter combat clothing with improved performance characteristics. To reduce labour and material costs for design and create an alternative to the experimental selection of the structure and composition of the material, a mathematical model of non-stationary heat transfer in the “environment – composite material – human” system is proposed. The problem of temperature distribution at any time for the outer and inner layers is presented in the form of heat transfer in a multilayer plate. The problem of temperature distribution in the heat-insulating layer of the material is presented in the form of heat transfer through a limited rod in the air. The developed mathematical model allows calculating the distribution of temperature fields in the layers of the material at different values of the effective heat flow and determine the limit parameters of its thermal protection effect.

Heat Removal and Thermal Stabilization of High-temperature Surfaces by a Dispersed Coolant Flow

The effectiveness of stabilizing the surface temperature by a dispersed coolant flow is experimentally studied on a bench simulating energy intensive elements of thermonuclear installations A test section in which the maximum heat flux density can be obtained when being subjected to high-frequency heating was developed, manufactured, and assembled. The test section was heated using a VCh-60AV HF generator with a frequency of not lower than 30 kHz. A hydraulic nozzle with a conical insert was used as the dispersing device. Techniques for carrying out an experiment on studying a stationary heat transfer regime and for calculating thermophysical quantities were developed. The experimental data were obtained in the stationary heat transfer regime with the following range of coolant operating parameters: water pressure equal to 0.38 MPa, water mass flow rate equal to 5.35 ml/s, and induction heating power equal to 6--19 kW. Based on the data obtained, the removed heat flux density and the heat transfer coefficients were calculated for each stationary heat transfer regime. The dependences of the heat transfer coefficient on the removed heat flux density and of the removed heat flux density on the temperature difference have been obtained. High values of heat transfer coefficients and heat flux density at a relatively low coolant flow rate were achieved in the experiments.

High-Power Heat Transfer in Supercritical Fluids

Non-stationary heat transfer in supercritical fluids at relatively small temporal and spatial scales was studied experimentally. The aim of the study was to clarify the peculiarities of conductive heat transfer mode at significant heat loads. An unexpected stepwise decrease in the instant heat transfer coefficient has been revealed in the course of crossing the vicinity of the critical temperature along the supercritical isobar. This means that the peaks of isobaric heat capacity and excess thermal conductivity, which are known from stationary measurements, do not affect the experimental results. It is assumed that the action of considerable gradient in temperature and the presence of heat-transfer surface in pulse heated system can serve as factors that suppress large-scale fluctuations, leading to a “smoothing” the critical enhancement of the thermophysical properties. As an important consequence, this study gives new insight into selection of the operating pressure of supercritical heat transfer agent.

Estimation Technique for a Contact Point Between two Materials in a Stationary Heat Transfer Problem

An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, of negligible diameter, made up of two consecutive sections of different, isotropic and homogeneous materials. At the left boundary, a Dirichlet type condition is imposed that represents a constant temperature source while a Robin type condition that models the heat dissipation by convection is considered at the right one. Many articles in the literature focus on thermal and stress analysis at the interface but no one is dedicated to the estimation of the contact point location between the two materials. In this work, it is assumed that the interface position is unknown. A technique to determine it from a unique noisy flow measurement at the right boundary is introduced. Necessary and sufficient conditions are derived in order to obtain the estimation of the interface point from a heat flux measured at the right boundary. Numerical solutions are obtained together with an expression for the estimation error. Moreover, an elasticity analysis is included to study the influence of data errors. The results show that our approach is useful for determining the location of the materials interface.

A source-sink approach for computation of intensity of low-potential underground heat non-stationary extraction

A new methodology for estimation of changing intensity characteristics of non-stationary heat transfer in underground heat extraction by a single-pipe upright heat exchanger is presented in this paper. Major trends in changing of a heat removal volume, linear heat transfer coefficient, linear heat transfer resistance, and heat sink radius have been estimated for specific ground types. Also a generalized one-factor linear semilogarythmic equation has been developed for specific ground types, along with an appropriate approximating function intended to simplify the underground heat extraction intensity estimation methodology.