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The paper presents a physico-mathematical model for determining the heat transfer parameters between viscous gasdynamic flotations and cooled gas turbine blades made using the technology of composite permeable membranes (CPM). The mathematical model includes equations of dynamic and thermal boundary layers taking into account injection, three-dimensional transient heat conduction in CPM cooled frames, complex hydraulic flow and cooling inside the channels of a cooled blade with air taken from the power plant compressor. A complex problem was solved to determine the thermal state of microrocket engines, where a method was proposed for immersing a multiply-connected domain in a region of the simplest form. A new economical, absolutely stable method is proposed for numerically solving of spatial nonstationary heat transfer problems in multiply-connected domains. The results obtained showed greater cooling efficiency at lower cooling medium costs. [ABSTRACT FROM AUTHOR]

Within this work, based on analyses of problems on wave heat transfer in bounded bodies, the theory of thermally isolated waves (solitons) is developed to investigate the heat transfer processes in the initial time vicinity and in the vicinity of the bounded body, that is the time scales are commensurate with the relaxation time (nanoseconds), and the scales of the spatial variable are measured in nanometers. A new analytical solution of the wave heat transfer based on the heat conduction equation of hyperbolic type under the action of a series of solitons was received, based on which the interaction of individual solitons with each other, absorption and reflection of the solitons from the body boundaries was analyzed. Analysis of a large number of results made clear that thermal solitons reflect not as mechanical ones, since first there is absorption of the soliton thermal energy by the heat-insulated boundary on the heat-insulated walls, and then the energy is rejected by the thermal conductivity in the opposite direction. It was found that the temperature gradient inside the soliton is negative in the forward direction and positive in the reflected direction. The results of the paper can be used in thermal interaction of high-power radiation with solid surfaces, as well as in the problems of quantum mechanics. [ABSTRACT FROM AUTHOR]

A closed mathematical model of heat and mass transfer under the non-isothermal filtration through the organized pores of coolants with a strong dependence of dynamic viscosity on temperature with further injection into a viscous gas-dynamic flotation with the formation of liquid film and evaporation under the influence of aerodynamic heat flows has been developed. The aim of the paper is to develop the physical and mathematical basis of thermal protection with the automatic supply of coolant having a strong dependence of dynamic viscosity on temperature (by 3-5 orders of magnitude when the temperature changes by 200-2500°C). Such thermal protection system allows for operating without the mass removal that preserves the geometry of the structural elements at the intensive heating, which is very relevant. To achieve this goal, a mathematical model of the automatic coolant supply with filtration through the organized pores, injection into a high-temperature gas-dynamic boundary layer with the formation of the protective liquid film and evaporation is formulated. The results with respect to the mass flow rate of the coolant, the mass evaporation rate of the formed liquid film and the temperatures of the structure which in all cases remain below the evaporation temperature of the cooler have been obtained. [ABSTRACT FROM AUTHOR]

Optimization of technological processes in metallurgy related to transfer and use of heat energy makes more complicated demands for calculation of heat exchange. Therefore, the work, the approximate analytical method for solving the conjugate problems of viscous gas-dynamic boundary layer and thermal conductivity in the anisotropic strip, has been developed. The paper uses modern numerical methods for solving differential equations in partial derivative and analytic methods on the basis of an integral transform of Fourier and Laplace. Boundary equations have been solved analytically with certain simplifications, and the problem of anisotropic heat conduction has been solved analytically. The heat flows are determined analytically by the longitudinal variable at the interface boundary. It has been established that temperature increase of the external surface contributes to that all factors directly impacting on the magnitude of heat flows act towards their reduction. The analytical solution for the problem of thermal conductivity in the anisotropic strip with a general type of anisotropy when the heat flows from the boundary layer are determined at the boundaries is obtained. The conducted research for the temperature of external boundary and heat flow from gas to it demonstrates that with increasing the degree of longitudinal anisotropy the surface temperature of the strip downstream increases from increasing longitudinal heat conduction An original conjugation method using the continuous heat flows, and temperatures at the interface boundary is found. The numerical results for the heat flows and temperatures at the interface boundary have been obtained and analyzed. [ABSTRACT FROM AUTHOR]

Within this work, based on the built analytical solution of heat transfer problem in anisotropic bodies, the thermal conductivity tensor components depending on temperature, the heat transfer is investigated under influence of a point heat source, inside a body or on a plane body surface. It turned out that heat transfer has a wave-like behavior with the presence of temperature front, where derivatives with respect to time and spatial variables are broken but they are continuous with respect to temperatures and heat flux. Besides, the heat wavefronts are ellipsoids in space and plane ellipsoids depending on time. Coordinates of heat wave velocity can be calculated, at that, velocities of front points are different in different directions. [ABSTRACT FROM AUTHOR]