Nonstationary Problem Of Heat Transfer Research Articles

Методика расчета тепловлагопереноса в специальной защитной обуви пожарного-спасателя

Разработана методика расчета тепловлагопереноса в специальной защитной обуви пожарного-спасателя, которая позволяет учесть терморегуляционные механизмы в стопе для оценки комфортности обуви, изготовленной из определенных пакетов материалов и эксплуатируемой в широком диапазоне внешних воздействий, как по тепловым и влажностным факторам, так и в зависимости от уровня активности (тяжести выполняемой работы) пожарного-спасателя. Для определения безопасной работы в специальной защитной обуви необходима оценка степени деструкции кожи (степень ожога). The article describes the solution of the problem of non-stationary heat transfer in the «foot – footwear – environment» system for multilayer flat, cylindrical or spherical materials and non-stationary heat transfer from the outer surface of the special protective footwear to firefighter's foot. The well-known biothermal equation and the generalized heat transfer equation are used as the basis for the model of heat and moisture transfer in boot materials, taking into account sweating on the human skin surface. It is possible to get data on the thermal state of the foot under various conditions by solving these equations with appropriate coefficients and boundary conditions: zero heat flow in the center of the foot and convective environmental conditions on the surface of the last layer of porous shoe material. Modeling for three cases of human activity: resting state, walking with a speed of 4.8 km/h, light work (in the office room) under the same environmental conditions was carried out. The obtained results showed that the model of heat and moisture transfer in protective boots, taking into account thermoregulatory processes in the foot, can be used to predict the functionality of the materials for the bottom and top of the boots in terms of the skin burns likelihood. The method for calculating heat and moisture transfer in special protective boots for a firefighter-rescuer has been developed, based on the simulation, which includes: - construction of a geometric image of a model of protective boots; - determination of the firefighter-rescuer operating mode; - selection of material packages for the details of the boot top and bottom. An indication of the thermophysical, structural, geometric characteristics of the materials allows, using the selected climatic conditions and the firefighter-rescuer operating mode, to establish the initial and boundary conditions for solving the basic system of heat and moisture transfer equations. The solution of the system of equations with the boundary and initial conditions makes it possible to assess the comfort of boots, as well as the rate of destruction of the skin under intense thermal effects (the probability of burns of varying degrees). Based on this analysis, further optimization of the boots design can be carried out by choosing different material packages or evaluating the thermal effect under various external influences.

Numerical study of microwave impact on gas hydrate plugs in a pipeline

Purpose. Development of a technique for the numerical study on the decomposition of gas hydrate plugs in deep-water pipelines under microwave radiation using a coaxial source. Theoretical efficiency evaluation of using such an impact to unblock the pipelines. Methodology. Mathematical modeling and computational experiment. Findings. An original mathematical model is proposed to describe heat transfer processes during the decomposition of gas hydrates in a pipeline under the action of heat sources distributed over the volume. The non-stationary problem of heat transfer was considered in a one-dimensional formulation. An algorithm for numerical computation is proposed. A mathematical expression is obtained for distributed heat sources generated by the microwave radiation from a coaxially located SHF antenna. Parametric numerical studies on temperature fields and decomposition dynamics of a gas hydrate plug are performed for specified parameters of pipe and microwave radiation power. The boundaries of the decomposition area and the dynamics of change in this area are determined. The decomposition time of a gas hydrate plug with a diameter of 0.3 m was determined using a 300 W microwave source. The complete decomposition took approximately 40 hours. Originality. The task of thermal decomposition of a cylindrical gas hydrate plug in a pipeline due to microwave heating using a coaxial microwave power source has been considered for the first time. The process is viewed as a sequence of several stages: heating, heating and decomposition, decomposition after complete heating of the gas hydrate layer. To model the volumetric dissociation of gas hydrate, it was proposed to use special functions that characterize the amount of decomposed gas hydrate. The introduction of such functions makes it possible to construct an efficient computational algorithm taking into account the action of volumetric sources in the decomposition area. The known models mainly consider only surface thermal effect or microwave impact on gas hydrate in porous mediums. The presented model allows describing the decomposition during volumetric heating of a solid hydrate adequately. Practical value. Blocking plugs may occur due to hydrate formation when transporting gas through deep-water pipelines or through pipelines in cold environments. The elimination of such complications is a complex technical task. In particular, a special source of microwave radiation, which was proposed by the authors in previous works, can be used to unblock the pipeline. The device that makes the microwave radiation is located along the pipe axis. The results of this work allow us to evaluate the effectiveness of the microwave method for eliminating the gas hydrate plug. The mathematical model and computational method can be used in the development of appropriate technologies using a coaxial microwave heating source.

Mathematical modeling of snacks drying process from minced fish in a fluidized bed

A mathematical model of snacks drying process from minced fish in a fluidized bed with distributed parameters of the heat exchange process between the surface of an anisotropic body and the environment is proposed. The solution of the problem of non-stationary heat transfer by heat conduction using the Galerkin method is considered. The trial and verification functions of the method used, implemented in the PTC MathCAD engineering calculation environment, are linearly independent, represent the first elements of a complete system of polynomial functions and satisfy the boundary and initial conditions. Theoretical and experimental studies have been carried out, which allow considering the process of drying snacks from minced fish in a fluidized bed and scientifically substantiate options for its improvement. According to the results of experimental studies, the adequacy of the obtained mathematical model is shown. It is proved that with a uniform initial temperature distribution during preheating, the temperature inhomogeneity increases up to the moment of a phase transition on the surface of dried object. The importance of taking into account the preheating phase of wet material is established, since at this stage a temperature profile is formed, which is characterized by significant heterogeneity. This is especially important, since temperature heterogeneity directly affects the quality of the food product. The possibility of taking into account anisotropy in heat transfer processes using a three-dimensional mathematical model of transport with distributed parameters is confirmed. The developed technique allows significantly increasing the accuracy of an anisotropic boundary value problem solving by replacing the operation of integrating the stiffness matrix elements with a system of differential equations by algebraic formulas.

Эффективность использования подземного пространства в суровых климатических условиях

The object of the study is rock masses with underground structures located in regions with a harsh climate. The subject of the study is the temperature in the rock mass in natural conditions and in the area where the structure is located, as well as the parameters of the energy efficiency of the underground facility. The purpose of the study is to determine the effect of thermal insulation and deepening of a structure from the surface on achieving the energy efficiency of underground facilities in regions with harsh climatic conditions. The tasks are to determine the temperature fields in the rocks of the northern regions and the rock temperature in the massif adjacent to the structure, to determine the loss of thermal energy with various technical characteristics of the underground structure. The method for determining the temperature fields in the rock massif and the loss of thermal energy by the structure is based on solving the non-stationary problem of heat transfer. The temperature fields are determined using the LIRA software package. The nature of temperature fluctuations of the rock layers closest to the surface in the conditions of the northern regions is considered. Temperature fluctuations on the contour of an underground structure are investigated. An assessment of the loss of thermal energy by an underground structure is being carried out. The influence of thermal insulation and deepening of the structure on its energy efficiency is determined. The field of application of the results of the study is related to the assessment of the energy loss of such underground structures as tunnels, refrigerators, parking lots, warehouses and other facilities. As a result of the research, it has been found that the rational use of underground space to the greatest extent depends on the quality of the thermal insulation of the object. A significant reduction in the loss of thermal energy by an underground structure is achieved with the simultaneous implementation of such measures as the use of thermal insulation and deepening of the object

МОДЕЛИРОВАНИЕ ДИНАМИКИ ТЕПЛОВОГО РЕЖИМА ТУПИКОВЫХ ГОРНЫХ ВЫРАБОТОК С ИСТОЧНИКОМ ВЫДЕЛЕНИЯ ТЕПЛОТЫ

Актуальность исследования обусловлена необходимостью снижения температуры воздуха в тупиковых горных выработках при ведении работ, связанных с выделением большого количества теплоты. Разработка способов нормализации термодинамических параметров рудничного воздуха в забоях на основе построения прогнозных математических моделей изменения теплового режима является необходимым условием обеспечения безопасности труда в горнодобывающей промышленности. Цель: получение зависимостей для определения скорости повышения температуры воздуха в тупиковой выработке при известных величинах интенсивности выделения теплоты и скорости её отведения вентиляционной струёй. Объекты: тупиковые выработки и окружающий породный массив. Методы: решение задачи нестационарного теплообмена рудничного воздуха и породного массива в сопряжённой постановке с помощью преобразований Лапласа; оценка безопасности по газовому фактору интенсификации выноса теплоты из горной выработки путём увеличения подачи воздуха в забой за счёт частично-повторного использования воздуха. Результаты. Проведён анализ проблемы отвода теплоты, выделяющейся при работе оборудования в замкнутом пространстве горных выработок. Показано, что процессов поглощения теплоты породным массивом и её отведения за счёт проветривания может быть недостаточно для обеспечения нормативных значений температуры воздуха. Разработана математическая модель сопряжённого теплообмена воздуха и породного массива, позволяющая прогнозировать повышение температуры с течением времени в зависимости от длины выработки и суммарной интенсивности выделения теплоты в ней. Установлено, что теплообменные процессы продолжительностью в несколько часов могут моделироваться в приближении малых времён, что значительно упрощает расчётные зависимости. Произведён расчёт динамики теплового режима при характерном для шахтных условий наборе физических параметров задачи, результаты которого явились обоснованием сделанного приближения и подтвердили опасность быстрого увеличения температуры воздуха при недостаточной скорости выноса теплоты из выработки вентиляционной струёй. Доказано, что при необходимости дополнительного отведения теплоты можно применять источники тяги высокой производительности с частично-повторным использованием исходящего воздуха без риска увеличения содержания газов в тупиковых выработках.

Temperature Field in a well in the Interval of Constant Gradients with Account for the Dependence of Thermal Conductivity on Temperature

The problem of nonstationary heat transfer of an ascending liquid flow is considered with account for the nonlinearity caused by the dependence of the thermal conductivity of oil on temperature. The method of solution represents a combination of the small parameter method with “on the average accurate” asymptotic method. By expanding in the small parameter and asymptotic parameters, the problem is reduced to a chain of linear problems. To determine the first coefficient of expansion in the small parameter, a special splitting procedure has been developed. With the aid of the developed apparatus of the small and formal parameters, analytical dependences of temperature in a well and surrounding rocks on time and spatial coordinates have been found that take into account the anisotropy of the thermophysical properties of media. It is shown that the zero approximation of the temperature function in the small parameter, as which the temperature coefficient γ is taken to be, coincides with the solutions of the corresponding linear problem with a constant value of the radial component of thermal conductivity λr, with the first approximation taking into account the contribution of nonlinearity to the solution obtained.

Temperature Effects on Polymer Structures of Canopies for Inversion Roofs of Multi-Storey Residential Buildings

The influence of temperature effects on the technical condition of cross-rod spatial structures of canopies for inversion roofs of multi-storey residential buildings made of polymer materials is considered on the example of tubular elements made of polyvinyl chloride (PVC). For modern multi-storey residential buildings, the current regulatory and technical documentation provides for operational (inversion) roofs, which can accommodate children’s sports grounds, cafes, bars, restaurants, parking lots, tanning salons, as well as gardens and architectural and landscape objects, helicopter platforms, etc. To protect visitors against atmospheric influences, canopies made of spatial core building structures (SCBS), which are operated in the open air, taking into account various climatic influences: high and low temperatures, corresponding humidity, precipitation, etc., are recommended. The elements of the core system are of the greatest interest for taking into account the temperature impact on the technical condition of the developed structure. The general solution of the problem of non-stationary heat transfer of a structure for calculating a two-dimensional temperature field is considered in a nonlinear formulation. The problem of thermal conductivity is considered under the assumption that there is a technical possibility for supplying a coolant inside the cylinder. As a result, there is a heat flow, with which it is possible to adjust the temperature between the outer and inner areas of the cylindrical elements for more efficient installation of the stress-strain state of the entire supporting structure as a whole.

INFLUENCE OF HEAT TREATMENT OF MOUNTAIN MASSIVE ON TEMPERATURE MODE OF GEOTHERMAL CIRCULATION SYSTEM

Based on the solution of the problem of non-stationary heat transfer during fluid motion in underground permeable layers, dependence was obtained to determine the operating time of the geothermal circulation system in the regime of constant and falling temperatures. It has been established that for a thickness of the layer H <4 m, the influence of heat influxes at = 0.99 and = 0.5 is practically the same, but for a thickness of the layer H> 5 m, the influence of heat inflows depends significantly on temperature. At a thickness of the permeable formation H> 20 m, the heat transfer at = 0.99 has virtually no effect on the thermal processes in the permeable formation, but at = 0.5 the heat influx, depending on the speed of movement, can be from 50 to 90%. Only at H> 50 m, the effect of heat influx significantly decreases and amounts, depending on the filtration rate, from 50 to 10%. The thermal effect of the rock mass with its thickness of more than 10 m, the distance between the discharge circuit and operation, as well as the speed of the coolant have almost no effect on the determination of the operating time of the GCS in constant temperature mode. During operation of the GCS at a dimensionless coolant temperature = 0.5, the velocity of the coolant is significant. With an increase in the speed of the coolant in two times, the error changes by 1.5 times.

Comparison of the analytical solutionof efficieтcy regenerative rotating heatexchangethe device with resultsof numericalcalculations

The article is devoted to the thermal-hydraulic calculation of the rotating heat exchanger of a gas turbine engine. More specifically, the purpose of this work is to determine the error of the known analytical calculation of the efficiency of the regenerative heat exchanger in comparison with numerical calculation. Analytical and numerical calculations of the rotating heat exchanger are performed. The main problem of creating a methodology for the analytical solution of processes occurring in rotating heat exchangers is that it is necessary to solve the problem of non-stationary heat transfer from the hot coolant to the coolant through the regenerator packing. The solution of any non-stationary process of heat transfer requires knowledge of the boundary and initial conditions of the process. As initial conditions, it is necessary to use the dependence of the regenerator packing temperature field on the steady state of its operation. Such a relationship can only be obtained after the calculation is completed. In this case, the solution of the heat transfer problem in a rotating heat exchanger is possible using two methodological approaches. The first possibility is a solution by successive approximations. In addition to the fact that such a technique is very time-consuming, it allows us to obtain only a numerical solution of the problem, the possibilities of analysis are limited. The second possibility is the use of one or several assumptions. Such an analytical solution was obtained by Stepanov G.Yu. It is clear that the use of assumptions in analytical analysis or in analytical calculations requires an assessment of the accuracy of the methodology. An estimate of the accuracy of the analytical solution to the efficiency of a rotating heat exchanger is given in the proposed work. It is shown that the error of the analytical solution of the regenerator efficiency in the zone of high regeneration degree values is insignificant in comparison with numerical calculations. Analytical solutions proposed by Stepanov G.Yu., are accessible and effective in the process of creating regenerators. Of particular importance are analytical calculations of the efficiency of regenerators when recording solutions in the form required by the similarity theory. An increase in the error in the analytical calculation of the efficiency of the regenerator is noted with a decrease in the ratio of the water equivalents of the heat-transfer packing of the rotating heat exchanger and coolants (gas and air). Marked increase of error of the analytical calculation of the effectiveness of the Regener-Torah in the decrease of water equivalent heat transfer gaskets. no-return heat exchanger and coolants (gas and air).

Development of the method of approximate solution to the nonstationary problem on heat transfer through a flat wall

In the present work, we propose a method for approximate analytical solution to the nonstationary problem of heat transfer through a flat wall in the concentrated statement. In the course of the study, three issues were consistently addressed: 1. symmetrical heating of a body, 2. asymmetrical heating, 3. nonstationary heat transfer. At the first stage, we solved in approximate analytical statement the problem on symmetrical heating of a plate. The solution obtained has an error. The availability in the scientific literature of exact analytical solution, in a distributed (one-dimensional) statement, allowed us to assess the accuracy of the obtained approximate solution. It does not exceed the limits permissible for engineering calculations. A special feature of the developed method is the possibility of its application as an integral part in solving the problems on nonstationary heat transfer. At the second stage, we solved a problem on asymmetrical heating of a plate. By using numerical study, the character of displacement of the minimum in temperature profile for thickness of the plate was identified. This made it possible, when applying the method developed at the previous stage, to obtain a solution to the problem on asymmetrical heating of the body. A special feature of the solutions is the developed approach to determining position of the temperature minimum for thickness of the plate. Such an approach was employed as another constituent part for solving a problem on nonstationary heat transfer. At the third stage, numerical study allowed us to identify a characteristic point of varying temperature profile and the trajectory of its motion in the process of nonstationary heat transfer. Based on these data and applying the developed method, we demonstrated the possibility of approximate analytical solution to the problem on nonstationary heat transfer through a flat wall. In all cases, when the exact solutions were lacking, assessment of error in approximate representation was conducted by comparing with the results of numerical calculations. The error did not exceed 6 %

THERMOTECHNICAL CALCULATION OF FLOORS ABOVE UNHEATED BASEMENT IN COTTAGE EXPLOITED UNDER INTERMITTENT HEATING CONDITIONS

The procedure of thermotechnical calculation of fl oor above unheated basement exploited under intermitt ent heating conditions is presented. Procedure in question is based on research of nonstationary problem of heat transfer through walling and takes into account thermo-inertial characteristics of walling materials. Through the example of fl oor above cottage basement is evaluated energy consumption and walling heating time in passing from stand-by mode to work mode with proposed procedure. Based on calculation results recommendations for energy and heating time saving are presented.

Application of the method of weighted residuals for determining the distribution of temperatures and radiation creep strains in plates

The paper is devoted to the description of the Weighted Residuals Method in Galerkin form for solution of the non-stationary heat transfer and irradiation creep problems in rectangular plates. The basic methods and dependencies were used for the solution of these problems are considered. The non-stationary heat problem is derived to sequential decisions of the systems of linear algebraic equations for the coefficients in expansions of temperature function in series on the basis functions for the different time moments. The problem of rectangular plate’s bending with specified temperature drops in its sides is preliminary solved in order to obtain the solution of irradiation creep problem. The stress tensor components were found in the plate’s points, are used in associated flow rule for the obtaining the components of creep irradiation strain tensor. The non-stationary heat transfer problem in quadratic area with boundary conditions of Newton and Diriclet types is considered as well as the calculated temperature distributions on co-ordinates in plane and time are presented. The irradiation creep of rectangular plate made from high resistant steel 15Х1М1Ф is considered. Obtained distributions of irradiation creep strains for three regarded values of temperature drops allow us to evaluate the plate deformation and service ability at different time moments.

Fully Automatic 2D hp -adaptive Finite Element Method for Non-stationary Heat Transfer

Abstract In this paper we present a fully automatic hp adaptive finite element method code for non-stationary two dimensional problems. The code utilizes the α -scheme for time discretization and fully automatic hp adaptive finite element method discretization for numerical solution of each time step. The code is verified on the examplary non-stationary problem of heat transfer over the L-shape domain. Acknowledgements The work of MP is supported by Polish National Science Center grant no. 2012/07/B/ST6/01229. The work of MS is supported by a Dean's grant.

The Error Characteristics When Determining the Temperature of Structural Transitions in Polymers

Structural transitions from one crystallographic modification to another occur in many polymers at temperatures below the melting point. Examples of different polymorphic multiplications in polytetrafluoroethylene (PTFE), polypropylene, caprolon B, polyvinylidenfluoride, etc., are known [1]. Thermomechanical analysis, differential scanning calorimetry, etc., are employed to investigate structural transitions in crystalline polymers. The majority of these methods are destructive, since they require the preparation of special samples made of the polymer material. There are nondestructive thermal monitoring methods, which enable one to determine the thermal properties of polymers and to record the structural transitions in them [2]. The method employed in the research described in this paper is based on an analytical solution of the boundary value problem of nonstationary heat transfer in a polymer, which occurs when it is heated with a plane circular source of heat of constant power. The method is based on the use of a data-measuring system (DMS) [3]. In probability theory, the characteristics which describe the properties of random quantities are determined using the integral expression [4]:

Нестационарный теплообмен в цилиндрическом канале при ламинарном течении жидкости

Using double integral Laplace–Carson transformation and orthogonal method of Bubnov–Galyorkin, the analytical solution of the non-stationary problem of heat transfer in a cylindrical channel in the laminar flow of fluids was obtained. It has two components: stationary and non-stationary, each part has application only in a certain range of temporal and spatial coordinates. For the stationary Graetz-Nusselt problem on the basis of introduction of the temperature perturbation front and additional boundary conditions it was managed to find an analytical solution that allows the assessment of liquid thermal state with small values of spatial variable, directed along the stream flow. It is not possible to obtain such results using the well-known exact analytical methods because of the poor convergence of infinite series of received solutions.

Nonstationary heat transfer in a hollow composite cylinder

Solution of a nonstationary heat-transfer problem for bounded end-conjugated hollow dissimilar cylinders is presented. In the volume of the cylinders, time- and coordinate-dependent heat release of known intensity takes place. The problem is solved using finite integral transformations over two coordinates.

Computational and experimental investigation of nonstationary heat transfer at a critical point

Similarity criteria are derived for the conjugate problem of nonstationary heat transfer, and the behavior of the heat transfer coefficient with a sharp change in the boundary conditions is studied.

One-dimensional stability of dissipative couette flow

Non-stationary one-dimensional flow, and especially the one-dimensional stability of a stationary Couette flow of a viscous incompressible fluid is considered, taking into account dissipative heat, under the assumption that the viscosity decreases fairly rapidly, e.g., exponentially, as the temperature incrases. It is shown that when the fluid is very viscous, the non-stationary plane problem can be reduced to a non-stationary problem of heat transfer in media with heat sources depending non-linearly on temperature. The dependence of the heat sources on temperature in the latter problem differs substantially for different types of boundary conditions in the initial problem. If a tangential stress is specified at the boundary, then the density of the heat sources will depend on temperature locally (such a problem was studied earlier in /1–6/. When the velocities of the boundary planes are given, the density of heat sources will depend on the temperature distribution as a whole, over the volume. As regards the stationary flow inspected here for stability, it does not always exist, nor is it unique /7–14/. We can utilize the results of /1, 2, 15–19/ by reducing the problem of the existence and uniqueness of such flow to the stationary problem of the temperature distribution in media with heat sources depending non-linearly on temparture.

Nonstationary problem of heat transfer in laminar-vacuum insulation

A mathematical model for nonstationary heat and mass transfer in multilayered insulation for the case of transverse evacuation of the packet is proposed. Results of numerical computations of the gas pressure, the shield temperature, and the heat flux in the packet for certain insulation variants are presented.