Inverse Problem Of Thermal Conductivity Research Articles

METHODOLOGY FOR STUDYING THE FIRE PROTECTION ABILITY OF A FIRE PROTECTION COATING BASED ON POLYSILOXANE AND OXIDES OF ALUMINIUM, TITANIUM, AND CHROMIUM FOR STEEL BUILDING STRUCTURES

Fires and their negative consequences are a significant problem today. The final report of the World Fire Statistics Centre in 2023 shows that an average of 3.7 million fires occurred annually between 1993 and 2021. The fire resistance of building structures has paramount importance and influence on the development and spread of fires in buildings and structures, which needs consideration at the design stage. Particular attention should be paid to metal structures when used in construction since their fire resistance limit is about 15 minutes, depending on the profile and cross-section of the structure, and this, in turn, limits their use in buildings and structures where the fire resistance class of structures is REI 15. A way to increase the fire resistance class of a steel building structure is its fire protection implemented using dedicated means that protect the steel structure from the effects of high fire temperatures. The study aims to develop a methodology and determine the heating time of prototypes of steel plates with a fire-retardant coating based on polysiloxane and oxides of aluminium, titanium, and chromium to a critical temperature depending on the coating thickness (0.3, 0.45, 0.6, 0.8 mm) and the thickness of the steel plate (0.3, 0.5, 0.8 cm). To determine the fire protection capacity of the developed fireproof coating, we used the method regulated by clause 7.4 of DSTU-N-P B V.1.1-29:2010 ‘Fireproof treatment of building structures. General requirements and control methods’. The authors have developed a methodology for conducting experimental studies of the effectiveness of fire protection coatings using an installation for determining the fire protection capacity (effectiveness) of fire protection coatings, the principle of which is to heat the interior of the installation chamber using electric heating elements. The heating time of the prototypes of steel plates with the developed fire protection coating to the critical temperature was determined, depending on the coating thickness and the thickness of the steel plate. We found that the extreme temperature in a steel plate with a thickness of 0.3 cm is reached at 23, 34, and 46 minutes with a coating thickness of 0.3, 0.45, and 0.6 mm, respectively. Experimental studies of steel plates with thicknesses of 0.5 and 0.8 cm have shown that with an increase in plate thickness at the same values of the thickness of the fire protection coating, the time to reach the extreme temperature increases by about 1 minute. At a coating thickness of 0.8 mm, for steel plates with thicknesses of 0.3 and 0.8 cm, the temperature on the unheated surface of the prototype did not reach the extreme value.Given the results obtained, it will be relevant to solve the inverse problem of thermal conductivity to determine the thermal and physical characteristics of the coating based on numerical data from experimental studies. Keywords: research methodology, standard temperature regime, fire protection coating, steel building structure.

THERMOPHYSICAL CHARACTERISTICS OF THE HVAF COATING FROM QUASICRYSTALLINE ALLOY OF THE Al-Cu-Fe SYSTEM

The article deals with the results of determining the thermal conductivity coefficient from quasicrystalline coatings of the Al-Cu-Fe system in the temperature range up to 900 °C. The Al-Cu-Fe quasicrystalline alloy acquires a great interest for practical use as a material for protective coatings. The Al-Cu-Fe alloy is used to produce thermal barrier coatings in internal combustion engines, non-stick coatings on chemical synthesis equipment and in the food industry and to prevent the icing in aviation. The Al-Cu-Fe quasicrystals have low density, high hardness, high elasticity modulus, high values of corrosion resistance and wear resistance, low coefficient of friction, lowered adhesion, low thermal conductivity in combination with the coefficient of thermal expansion, which is close by its value to some metals. The water atomized Al63Cu25Fe12 powder with a dispersion of +40/-63 μm that has a content of the quasicrystalline phase of about 60 wt. % was used for spraying. The coating was sprayed to the butt of a cylindrical substrate from steel 45 (diameter – 25 mm, height – 10 mm), which before spraying was subjected to jet-abrasive treatment by corundum powder with a determining particle size of 1 mm at air pressure of spraying of 0.5 MPa. The Al-Cu-Fe coating with a thickness of more than 0.8 mm was made by high-speed air-fuel (HVAF) spraying using a burner GVO-RV12 with the following spraying mode: the pressure in the combustion chamber of the burner is 1.0 MPa; the oxidant excess coefficient a ≈ 1.2, the spraying distance is 270 mm. The samples were installed on the side surface of the drum (diameter 120 mm), which rotates at a speed of 2.0 rev/s (the speed of movement of the sputtering spot is 0.8 m/s). Spraying was done in three steps of 10 seconds each with a 30 second cooling time between them. Determination of the temperature dependence of the thermal conductivity of the coating was carried out by solving the inverse problem of thermal conductivity by one-dimensional temperature fields in samples obtained by single-sided jet heating with an industrial hot air torch (at surface temperatures up to 450 °C) and an oxygen-propane welding torch (at temperatures above 450 °C). It is shown that the values of the thermal conductivity coefficient of Al-Cu-Fe quasicrystalline coatings in the range of 20 °С…900 °С vary within λ = 1.9 – 2.31 W/(m×K).

THERMOPHYSICAL CHARACTERISTICS OF THE HVAF COATING FROM QUASICRYSTALLINE ALLOY OF THE Al-Cu-Fe SYSTEM

The article deals with the results of determining the thermal conductivity coefficient from quasicrystalline coatings of the Al-Cu-Fe system in the temperature range up to 900 °C. The Al-Cu-Fe quasicrystalline alloy acquires a great interest for practical use as a material for protective coatings. The Al-Cu-Fe alloy is used to produce thermal barrier coatings in internal combustion engines, non-stick coatings on chemical synthesis equipment and in the food industry and to prevent the icing in aviation. The Al-Cu-Fe quasicrystals have low density, high hardness, high elasticity modulus, high values of corrosion resistance and wear resistance, low coefficient of friction, lowered adhesion, low thermal conductivity in combination with the coefficient of thermal expansion, which is close by its value to some metals. The water atomized Al63Cu25Fe12 powder with a dispersion of +40/-63 μm that has a content of the quasicrystalline phase of about 60 wt. % was used for spraying. The coating was sprayed to the butt of a cylindrical substrate from steel 45 (diameter – 25 mm, height – 10 mm), which before spraying was subjected to jet-abrasive treatment by corundum powder with a determining particle size of 1 mm at air pressure of spraying of 0.5 MPa. The Al-Cu-Fe coating with a thickness of more than 0.8 mm was made by high-speed air-fuel (HVAF) spraying using a burner GVO-RV12 with the following spraying mode: the pressure in the combustion chamber of the burner is 1.0 MPa; the oxidant excess coefficient a ≈ 1.2, the spraying distance is 270 mm. The samples were installed on the side surface of the drum (diameter 120 mm), which rotates at a speed of 2.0 rev/s (the speed of movement of the sputtering spot is 0.8 m/s). Spraying was done in three steps of 10 seconds each with a 30 second cooling time between them. Determination of the temperature dependence of the thermal conductivity of the coating was carried out by solving the inverse problem of thermal conductivity by one-dimensional temperature fields in samples obtained by single-sided jet heating with an industrial hot air torch (at surface temperatures up to 450 °C) and an oxygen-propane welding torch (at temperatures above 450 °C). It is shown that the values of the thermal conductivity coefficient of Al-Cu-Fe quasicrystalline coatings in the range of 20 °С…900 °С vary within λ = 1.9 – 2.31 W/(m×K).

Preheating of secondary superheated steam pipelines when starting steam turbines of SCР power units

Specific features of the technology of preheating hot legs of steam pipelines of intermediate steam overheating at the start-up of SCР power units with single-bypass thermal circuits are presented, with the advantages and disadvantages of various previously used methods of preheating steam pipelines after intermediate steam overheating at the startup of power units at supercritical pressure with a capacity of 250–300 MW considered. The analysis of the conditions for the completion of the heating of these steam pipelines using various process heating arrangements, as well as the heating steam consumption necessary for heating and its sources (special kindling steam by-passes, steam by-passes of own needs, kindling expander and combined heating technology at various intermediate rotational speeds of the turbine rotor) is carried out. The results of computational and experimental studies of the heating processes of steam pipelines during the start-up of SCР power units from various thermal states are presented, nomograms for determining the duration of preheating of mono and double steam pipelines with a capacity of 250–300 MW, developed on the basis of solving the inverse problem of thermal conductivity, are presented. The basis for determining the duration of heating of steam pipelines is the assumption of limited cooling of the medium pressure rotor of the steam turbine as steam is supplied to the same, as well as the temperature of the end section of the steam pipeline, which excludes the formation of condensate and thereby reduces the risk of its removal into the flow part when steam is supplied to the medium pressure cylinder. Two criteria for the termination of heating are determined in the form of an average integral temperature of the middle part of the steam pipeline and the temperature of its end section upstream the steam inlet elements of the medium pressure part.

Method for determining the thermal diffusivity and thermal conductivity coefficient by temperatures of plate surface as a semi-bounded body

The studied numerical and analytical model of a semi-bounded body is used to simultaneously determine the thermophysical characteristics (TFC): thermal diffusivity at and thermal conductivity coefficient λt of the material which make it easy to determine the volumetric heat capacity сt . Temperature distribution over the plate cross-section at the end of the calculated time interval τ is described by a power function, its exponent n depends on the Fourier number Fo. The values of TFC were calculated from the dynamics of changes in surface temperatures T(xp = Rp , τ) and T(xp = 0, τ) of the plate with a thickness Rp heated under boundary conditions of the second kind q = const. The temperature T(xp = 0, τ) was used to determine the time moment τe , at which the temperature perturbation reached the adiabatic surface xp = 0 (T(Rp , τe ) – Tb (0, τe = 0) = 0.1 K). Calculations of TFC (at and λt ) were performed using formulas whose parameters were found by solving a nonlinear system of three algebraic equations by selecting the Fourier number corresponding to τe . The author studied the complexity and accuracy of TFC calculation using the test (initial) temperature fields of a plate made of refractory material by the finite difference method. Dependences of TFC on the temperature ai (T ), λi (T ) and ci (T ) were set by polynomials. Temperatures of the plate with a thickness of Rp = 0.04 m with initial conditions Tb = T(xp , τ = 0) = 300, 900, 1200, 1800 K (0 ≤ xp ≤ Rp ) were calculated for a specific heat flow q = 5000 W/m2. The heating time to τe was 105 – 150 s. The average mass temperature Tm, pl of the plate during the τe increased by 5 – 11 K. The TFC values were restored by solving the inverse thermal diffusivity problem for 10 time points τi + 1 = τi + Δτ. The arithmetic mean deviations of TFC (Tm, pl ) from the initial values for calculations at Tb = 300, 900, 1200, 1800 K were less than 2.5 %. It was established that the values of at and λt obtained for the time moments ti are practically constant, therefore, a simplified calculation of at, o and λt, o is possible only from the values of temperatures T(Rp , τe ) and T(0, τe ) at the end of heating. The values of at, o and λt, o , which were calculated immediately for the entire heating time, differed from the initial values of the accepted heat exchange conditions by about 2 %. The parameters of simple algebraic formulas for calculating at, o and λt, o were found by solving a system of three nonlinear equations n = n( Fo), at, o = a(Tb , T(Rp , τe ), Rp , n, τe ), Fo = Fo(at, o , Rp , τe ) and expressions for λt, o = λ(Rp , q, n, Tb , T(Rp , τe )). The proposed method significantly simplifies the solution of the inverse problem of thermal conductivity.

The Solving of the Inverse Thermal Conductivity Problem for Study the Short Linear Heat Pipes

The results of studies by solving the inverse thermal conductivity problem of the heat capacity of evaporator of the short linear heat pipes (HP’s) with a Laval nozzle-liked vapour channel and intended for cooling spacecraft and satellites with strict take-off mass regulation are presented. Mathematical formulation of the inverse problem for the HP’s thermal conductivity in one-dimensional coordinate system is accompanied by the measurement results using the monotonic heating method in a vacuum adiabatic calorimeter the HP’s surface temperatures along the longitudinal axis over the entire temperature load range, thermal resistance, and arrays of thermal power data on the evaporator Qev and vortex flow calorimeter Qcond for the condensation surface allow us to estimate the average value of the evaporator heat capacity Cev by solving the inverse thermal conductivity problem in the HP’s evaporator region. Since at the beginning of working fluid boiling for a certain time interval, the temperature of the capillary-porous evaporator remains close to constant, and with the continuation of heating and by solving the inverse thermal conductivity problem, it becomes possible to calculate the heat capacity of the working evaporator and the evaporation specific heat of the boiling working fluid and compare it with the table values.

Применение инженерных методов расчета параметров методических печей для режимов с пониженной производительностью

A method has been developed for determining the rational operating parameters of continuous furnaces for rolling production, under which, under conditions of reduced productivity, a given temperature and uniformity of metal heating are ensured and excessive fuel consumption is excluded. The development is based on the improvement of well-known engineering methods for calculating methodical furnaces. The establishment of rational heating modes is a reserve for reducing fuel consumption, reducing economic costs and increasing the level of energy efficiency of the process as a whole. The use of engineering calculation methods to achieve this goal is due to the need to alleviate the problems associated with solving the inverse problem of thermal conductivity and the direct use of the developed algorithms within the ACS to control processes in real time.
 To check the correctness of the results obtained using the improved engineering technique, their verification is implemented using a mathematical model that solves the direct problem of thermal conductivity according to an explicit finite-difference scheme. The results obtained showed that in the investigated range of decrease in furnace productivity, the establishment of the proposed temperature profile allows reaching the required characteristics of the temperature field of the blanks.The threshold value of productivity has been determined, below which the required temperature of the workpieces is guaranteed to be reached. It is concluded that it is necessary to continue research to adapt the calculation method to the conditions of real production, as well as to optimize modes with productivity below the threshold value. The results obtained can be used to design new automated process control systems (APCS) or to improve existing ones.

Теплофизические характеристики теплозащитного материала корпуса ракетного двигателя при температурах до 1000 оС

An experimental determination of the temperature dependences of the specific heat capacity and the thermal conductivity coefficient of the multifunctional coating MFP-92 at temperatures up to 1000 °C has been carried out. At temperatures up to 450 °C, an IT-c-400 device was used to determine the specific heat capacity. IT-l-400 device was used for the determination of thermal conductivity. At higher temperatures, the determination of the thermophysical characteristics (TPC) was carried out by solving the inverse problem of thermal conductivity (IPT) in a flat plate under conditions of one-sided heating in a muffle furnace. Composite material MFP-92 is a multilayer structure with upper layers based on silica fabric and chromophosphate binder and lower layers based on mullite-silica fabric and aluminosilicate binder. The TPC of the layers also differ from each other, and, accordingly, the properties of this material as a whole can be determined only in the form of their effective values, averaged in one way or another over the thickness of the coating. In addition, during heating, the material undergoes significant physicochemical transformations associated with the thermal destruction of its components, manifested in the form of abundant gas release, and a decrease in the density of the material, which significantly changes its TPC and determines its dependence on the heating rate. Therefore, studies of the thermophysical characteristics of the MFP-92 material were carried out with several (2-5) consecutive heating cycles. It was found that in four heating cycles of the MFP-92 material up to 450 °C for 75 minutes when measuring the specific heat on the IT-c-400 device, its temperature dependence significantly changes qualitatively and quantitatively. With furnace heating to 1000 °C, the temperature dependences of the TPC of the material, determined in the first and second heating cycles, have a different form, but change insignificantly in subsequent heating cycles. This makes it possible to ascribe to the MFP-92 material a set of two sets of TPC related to its initial (phase A) and annealed after heating to 1000 °C (phase B) states. Using the obtained TPС of phase A (including the magnitude of the thermal effect of irreversible endothermic phase transition at 100 °C) and phase B, good agreement was obtained between the calculated and experimental temperature fields in the samples under furnace heating conditions.

Оценка огнестойкости стальных строительных конструкций с учетом влияния теплообмена с примыкающими смежными конструкциями

Purpose. On the basis of experimental studies and theoretical data, to determine the thermophysical characteristics of an intumescent fire retardant and evaluate the heating of steel structures with intumescent fire protection of the outer surface, taking into account the adjoining of a concrete coating, as well evaluate the effect of heat transfer with a concrete coating on the optimal layer thickness of an intumescent fire retardant to ensure the required fire resistance limit. Methods. Modeling in the system of finite element analysis. Findings. On the basis of a series of experimental and theoretical studies in the ANSYS finite element analysis system, the thermotechnical problem of fire resistance of steel structures with fire protection of the outer surface based on an intumescent composition was solved, taking into account the abutment of a concrete coating. Experimental studies are used to assess the effective values of the thermophysical characteristics of an intumescent composition by solving the inverse problem of thermal conductivity for a computational finite element model using parametric optimization methods. The obtained thermophysical characteristics made it possible to evaluate the heating of steel structures with fire protection, taking into account heat transfer with a concrete coating. Depending on the required fire resistance level and the type of the considered structures (floor slab) and the design situation, taking into account heat exchange with the concrete coating, the optimal thickness of the fire retardant coating that provides the required fire resistance level is reduced by 1.2 ... 4.4 times. Application field of research. The results can be used to solve the fire resistance problems of steel structures with partial and full fire protection of the outer surface during the design and construction of buildings and structures.

INVESTIGATION OF TEMPERATURE FIELDS DURING PLASMA-MECHANICAL PROCESSING OF LARGE-SIZED PARTS

A method for determining the temperature field in the near-surface zone of parts during plasma-mechanical processing, based on solving the inverse problem of thermal conductivity, using the results of model experiments in laboratory conditions, has been developed and implemented. The obtained experimental results allowed us to determine the optimal processing modes.

Determination of thermal diffusivity of the material by numerical-analytical model of a semi-bounded body

A mathematical description of the material thermal diffusivity aт in a semi-bounded body is proposed with a relatively simple algorithm for its numerical and analytical by solving the inverse problem of thermal conductivity. To solve the problem, it is necessary to obtain the temperature values of the unbounded plate as a result of a thermophysical experiment. A plate can be conditionally considered as a semi-bounded body as long as the Fourier number Fo ≤ Foк (Foк ≈ 0.04–0.06). It is assumed that the temperature distribution over cross-section of the heated layer of the plate R is sufficiently described by a power function whose exponent depends linearly on the Fourier number. A simple algebraic expression is obtained for calculating aт in the time interval ∆τ from the dynamics of temperature change T(Rп , τ) of a plate surface with thickness Rп heated under boundary conditions of the second kind. Temperature of the second surface of the plate T(0, τ) is used only to determine the time of the end of experiment τк. The moment of time τк, in which the temperature perturbation reaches the adiabatic surface x = 0, can be set by the condition T(Rп , τк) – T(0, τ = 0) = 0,1 K. The method of approximate calculation of dynamics of changes in depth of the heated layer R by the values of Rп , τк , and τ is proposed. Calculation of a т for the time interval ∆τ is reduced to an iterative solution of a system of three algebraic equations by matching the Fourier number, for example, using a standard Microsoft Excel procedure. Estimation of the accuracy of a т calculation was made by the test (initial) temperature field of the refractory plate with the thickness Rп = 0.05 m, calculated by the finite difference method under the initial condition T(x, τ = 0) = 300 (0 ≤ x ≤ Rп) at radiation-convective heating. The heating time was 260 s. Calculation of aт, i was performed for 10 time moments τi + 1 = τi + Δτ, τ = 26 s. Average mass temperature of the heated layer for the whole time was T = 302 K. The arithmetic-mean absolute deviation of aт(T = 302 K) from the initial value at the same temperature was 2.8 %. Application of the method will simplify the conduct and processing of experiments to determine the thermal diffusivity of materials.

Determination of Thermal Diffusivity of Material by the Numerical-Analytical Model of a Semi-Bounded Body

A mathematical description of a material’s thermal diffusivity ae in a semi-bounded body is proposed with a relatively simple algorithm for its numerical and analytical calculation by solving the inverse problem of thermal conductivity. To solve the problem, it is necessary to obtain the temperature values of the unbounded plate as a result of a thermophysical experiment. A plate can be conditionally considered as a semi-bounded body as long as Fourier number Fo ≤ Foe (Foe = 0.04–0.06). It is assumed that the temperature distribution over a cross-section of the heated layer of the plate with thickness R is sufficiently described by a power-like function whose exponent depends linearly on the Fourier number. A simple algebraic expression is obtained for calculating ahc in time interval Δτ from the dynamics of temperature change T(Rp, τ) of a plate surface with thickness Rp heated at boundary conditions of the second kind. Temperature T(0, τ) of the second surface of the plate is used only to determine end time τe of the experiment. Moment of time τe, at which the temperature perturbation reaches adiabatic surface x = 0, can be set by the condition T(Rp, τe) – T(0, τ = 0) = 0.1 K. An approximate method of calculating the dynamics of changes in depth of heated layer R by values of Rp, τe, and τ is proposed. The calculation of ahc for time interval Δτ is reduced to an iterative solution of a system of three algebraic equations by matching the Fourier number, for example, using a standard Microsoft Excel procedure. Estimation of the accuracy of calculation of ahc at radiation-convective heating was performed using the initial temperature field of the refractory plate with thickness Rp = 0.05 m, calculated by the finite difference method under initial condition T(x, τ = 0) = 300 (0 ≤ x ≤ Rp). The heating time was 260 s. Calculation of ahc, i has been performed for ten time moments τi + 1 = τi + Δτ, Δτ = 26 s. Average mass temperature of the heated layer for the entire time was τe T = 302 K. The arithmetic-mean absolute deviation of ae (T = 302 K) from the initial value at the same temperature was 2.8%. Application of the method will simplify conducting and processing experiments to determine thermal diffusivity of materials.

Experimental and Theoretical Research of a Hot Condition of High Pressure Cylinder of the T-100-130 Steam Turbine

The results of experimental and theoretical studies of the temperature state of the high- pressure cylinder (HPC) of the T-100-130 steam turbine for one of the start modes are presented. Taking into account the dependence of the coefficient of linear expansion on the temperature, the elongations of the individual sections of the casing under different temperatures and its total elongation after the turbine operation starts to correspond to the stationary operation mode have been found. The studies have shown that in the process of actuation the turbine there is a significant difference in temperature along the length of the HPC casing. In this case, the most intense heating occurs in the area from the second to the sixth section. The greatest temperature difference was observed in stationary operation at maximum temperature in the fifth section. Using the orthogonal method of L. V. Kantorovich, an approximate analytical solution of the thermal conductivity problem for a two-layer wall (turbine casing – thermal insulation) under inhomogeneous boundary conditions of the third kind is obtained. With the use of experimental data on the temperature state of the outer surface of the casing of the HPC by solving the inverse problem of thermal conductivity, the average heat transfer coefficients for the actuation period characterizing the intensity of heat transfer from steam to the casing have been found. On the basis of experimental data on the temperature change of any of the controlled parameters of the turbine over time, a theoretical method for predicting its change in a certain time range from the time of the its last measurement has been developed. The use of this method to predict the change in the temperature difference between the top and bottom of the HPC casing during the actuation showed that for a period of time equal to 3–5 minutes the forecast is fulfilled with high reliability.

DETERMINING HEAT TRANSMISSION RESISTANCE OF ENCLOSING STRUCTURES

Fulfillment of the activities aimed to an increase of the thermal resistance of enclosing structures requires the determination of their thermophysical characteristics with the use of the determination method based on the solution of problems of heat conduction, establishing the con- nection between the spatial and temporal temperature changes under the effect of heat source. This work uses the solution of the problem under nonstationary heating of the enclosing structure in the form of unrestricted plate with boundary conditions of the III kind. According to the known relations and graphs alterations in surface temperature depending on warm-up time, on thermal resistance of constructions and on arguments of Fo and Bi, i. e. initial and boundary conditions are determined. The graphic dependencies that have been obtained show that the surface temperature depends on the thermal resistance, while the temperature at the opposite surface during heat expo- sure remains practically unchanged during t = 5 h. Thus, if the outside air temperature is altered, then the rate of change of surface temperature or relative temperature q make it possible to deter- mine the thermophysical characteristics by solving the inverse problem of thermal conductivity with the use of the converted ratio to determine R as a function R = f(q, t). If the constructed graphic dependencies R = f(q, t) are used at different heat transfer coefficients, then according to the measured temperatures at different time intervals it is possible to determine thermal resistance in the same time intervals and, according to their average value, determine the required resistance to heat transfer R. The estimated ratio of analytical and graphic dependencies that we have obtained demonstrate the adequacy of the conducted full-scale measurements, if the areas with homogeneous temperature field and temperature history are chosen, and they can be used in determining the heat resistance of the enclosing structure in the form of unrestricted plate with boundary conditions of the III kind.

Unsteady heat transfer during subcooled film boiling

Cooling of high-temperature bodies in subcooled liquid is of importance for quenching technologies and also for understanding the processes initiating vapor explosion. An analysis of the available experimental information shows that the mechanisms governing heat transfer in these processes are interpreted ambiguously; a more clear-cut definition of the Leidenfrost temperature notion is required. The results of experimental observations (Hewitt, Kenning, and previous investigations performed by the authors of this article) allow us to draw a conclusion that there exists a special mode of intense heat transfer during film boil- ing of highly subcooled liquid. For revealing regularities and mechanisms governing intense transfer of energy in this process, specialists of Moscow Power Engineering Institute’s (MPEI) Department of Engineering Thermal Physics conduct systematic works aimed at investigating the cooling of high-temperature balls made of different metals in water with a temperature ranging from 20 to 100°C. It has been determined that the field of temperatures that takes place in balls with a diameter of more than 30 mm in intense cooling modes loses its spherical symmetry. An approximate procedure for solving the inverse thermal conductivity problem for calculating the heat flux density on the ball surface is developed. During film boiling, in which the ball surface temperature is well above the critical level for water, and in which liquid cannot come in direct contact with the wall, the calculated heat fluxes reach 3–7 MW/m2.

Cuboids of Infrared Images Reduction

The main idea of this scientific article is tomography usage. Projections of multidimensional signal carrying the information about the spatial structure of objects' thermal physic properties are represented by thermal tomograms obtained in active mode of test material surface heating by infrared radiation. Processing of a thermal tomogram is produced by solving the inverse thermal conductivity problem. This solution applies to cuboids of infrared images reduction class of problems. Because of reduction, we get the distribution image of thermal conductivity identified values on isotropic material surface (thermal tomogram) allowing revealing foreign inclusions in the heterogeneous object structure based on the contrast over thermal conductivity. Implementation of this idea is associated with certain difficulties due to the necessity of mathematical modeling of nonlinear thermal transients. The paper presents quartz sand thermal tomograms with temperature conductivity of 9 10-7 m2 s and thermal conductivity of -1 0.9 W m-1 K-1 which structure contains thermal insulation material - expanded foam, and thermally conductive material - aluminum.

Global correlation between surface heat fluxes and insolation in the 11-year solar cycle: The latitudinal effect

Because of the small amplitude of insolation variations (1365.2–1366.6 W m−2 or 0.1%) from the 11-year solar cycle minimum to the cycle maximum and the structural complexity of the climatic dynamics, it is difficult to directly observe a solar signal in the surface temperature. The main difficulty is reduced to two factors: (1) a delay in the temperature response to external action due to thermal inertia, and (2) powerful internal fluctuations of the climatic dynamics suppressing the solar-driven component. In this work we take into account the first factor, solving the inverse problem of thermal conductivity in order to calculate the vertical heat flux from the measured temperature near the Earth’s surface. The main model parameter—apparent thermal inertia—is calculated from the local seasonal extremums of temperature and albedo. We level the second factor by averaging mean annual heat fluxes in a latitudinal belt. The obtained mean heat fluxes significantly correlate with a difference between the insolation and optical depth of volcanic aerosol in the atmosphere, converted into a hindered heat flux. The calculated correlation smoothly increases with increasing latitude to 0.4–0.6, and the revealed latitudinal dependence is explained by the known effect of polar amplification.

Determination of the contact thermal resistance from the solution of the inverse problem of thermal conductivity

The contact resistance at the boundary between an orthropic reinforcing rod and an isotropic matrix is determined from the solution of the inverse probblem of thermal conductivity, using the gradient method. The suggested modification of the computational algorithm as the initial calculation of the initial period of the thermal process is shown to enhance the resolving power of the method and the choice of zeroth approximations from below is shown to ensure monotonic convergence of the solution.

Uniqueness conditions and method of solution of the coefficient inverse problem of thermal conductivity

The uniqueness conditions are formulated for the coefficient problem of thermal conductivity and an approach to devising the algorithm for solving it is presented.

Solution of the nonlinear inverse thermal conductivity problem by the iteration method

A regular iteration algorithm is constructed for the case of a nonlinear generalized thermal conductivity equation for determination of the nonstationary thermal flux. The algorithm is based on the method of conjugate gradients.