RESEARCH OF THE TEMPERATURE FIELD IN THE SYSTEM OF MULTILAYER CYLINDRICAL SOLID BODIES UNDER FIRE CONDITIONS

Introduction. The current urgent task is to find the temperature field distribution in cylindrical structures such as "solid cylinder inside a multilayer cylindrical shell". A characteristic feature of such structures is different mechanical and thermophysical characteristics of the layers combination, which makes them more perfect. However, this approach causes significant difficulties in developing analytical methods for their study. Therefore, new research methods development for multilayer, in particular, cylindrical structures is an urgent task today.Purpose. Direct method is used to study the heat transfer processes in the system "one-piece cylinder inside a multilayer cylindrical shell".Methods. To solve the initial parallel, the auxiliary problem of determining the distribution of a nonstationary temperature field in a multilayer hollow cylindrical structure with a "removed" cylinder of a sufficiently small radius is set. The solution of the auxiliary problem is realized by applying the method of reduction using the concept of quasi-derivatives. The Fourier schemeis used by using a modified method of eigenfunctions.Results. To find the solution to the problem, we used the idea of a boundary transition by directing the radius of the removedcylinder to zero. It is established that in this approach, all eigenfunctions of the corresponding problem have no singularities atzero, which means that the solutions of the original problem are limited in the whole structure. To illustrate the proposed method,a model example of finding the temperature field distribution in a four-layer column of circular cross-section (tubular concretecolumn) under the influence of the standard temperature of the fire. The results of the calculations are presented in the form of athree-dimensional graph of temperature changes depending on time and spatial coordinates.Conclusions. A direct method was used to solve the initial problem, using the idea of a boundary transition for the first time.In the general formulation (the function of changing the temperature of the environment is considered arbitrary, no restrictionsare imposed on the thickness of the shell and the number of layers) such a problem is solved for the first time.The structure of the obtained explicit exact formulas allows creating an algorithm for calculating the temperature field inthe form of automated programs, where it is enough to enter the initial data. Note that such algorithms include: a) calculating theroots of the characteristic equation; b) multiplication of a finite number of known matrices; c) calculation of definite integrals; d)summation of the required number of members of the series to obtain a given accuracy of the calculation.

AN ANALYTICAL MODEL OF A NON-STATIONARY TEMPERATURE FIELD IN A RESERVOIR WITH A HYDRAULIC FRACTURING

At the present stage of development of the oil and gas industry, considerable attention is paid to methods of increasing oil recovery of productive reservoirs. One of the most popular methods of intensifying oil production today is hydraulic fracturing. The efficiency and success of hydraulic fracturing largely depends on the parameters of the formed fracture; in this regard, the development of methods for evaluating the parameters of hydraulic fracturing fractures is an urgent task. Non-stationary thermometry is a promising area for monitoring the quality of hydraulic fracturing. To date, thermometry is used to localize the locations of multiple fractures in horizontal wells. In this paper, we study the application of non-stationary thermometry for estimating the parameters of a vertical hydraulic fracturing fracture. An analytical model of non-isothermal single-phase fluid filtration in a reservoir with a vertical fracture is developed. To calculate the temperature field in the formation and the fracture, the convective heat transfer equation is used, taking into account the thermodynamic effects (Joule — Thomson and adibatic), for the fracture, the heat and mass transfer between the fracture and the formation area is also taken into account. To assess the correctness of the model, the analytical solution is compared with the results of numerical modeling in the Ansys Fluent software package. The nonstationary temperature field is calculated for the constant sampling mode. It is established that at the initial moment of time after the well start-up, a negative temperature anomaly is formed due to the adiabatic effect, the value of which increases with a decrease in the fracture width. Over time, the temperature of the fluid flowing into the well increases due to the Joule — Thomson effect, and the value of the positive temperature anomaly increases as the width and permeability of the fracture decreases due to an increase in the pressure gradient in it. The developed analytical model can be used to solve inverse problems for estimating hydraulic fracturing parameters based on non-stationary temperature measurements in the wellbore of producing wells.

Modeling of the Two-Dimensional Thawing of Logs in an Air Environment

A two-dimensional mathematical model has been created, solved, and verified for the transient nonlinear heat conduction in logs during their thawing in an air environment. For the numerical solution of the model, an explicit form of the finite-difference method in the computing medium of Visual FORTRAN Professional has been used. The chapter presents solutions of the model and its validation towards own experimental studies. During the validation of the model, the inverse task of the heat transfer has been solved for the determination of the logs’ heat transfer coefficients in radial and longitudinal directions. This task has been solved also in regard to the logs’ surface temperature, which depends on the mentioned coefficients. The results from the experimental and simulative investigation of 2D nonstationary temperature distribution in the longitudinal section of poplar logs with a diameter of 0.24 m, length of 0.48 m, and an initial temperature of approximately –30°C during their many hours thawing in an air environment at room temperature are presented, visualized, and analyzed.

SIMULATION OF HEAT EXCHANGE IN A MULTILAYER FLAT STRUCTURE UNDER PERFECT THERMAL CONTACT IN FIRE CONDITIONS

The proposed work is devoted to the application of the direct method to the study of heat transfer processes in a multilayer flat structure. It is assumed that each layer is made of isotropic material of different thickness. There is an imperfect thermal contact between them, and the layers have internal heat sources. In this case, the isothermal surfaces are parallel planes, i.e the temperature changes in only one direction. On the outer surfaces of the structure there is a convective heat exchange with the environment, i.e the boundary conditions of the third kind are fulfilled. The coefficients of the thermal conductivity equation are considered to be piecewise constant with respect to the spatial coordinate. This is the first time the problem has been solved in this setting. The solution of the problem is realized by applying the method of reduction using the concept of quasi-derivatives and applying the theory of systems of differential equations with impulse action. The following is the procedure for separating Fourier variables using a modified method of eigenfunctions.Based on the physical content of the problem, the differential equation of thermal conductivity was written in the Cartesian coordinate system, but the solution scheme presented here without any fundamental difficulties extends to similar problems for multilayer bodies of basic geometric shapes by switching to appropriate coordinate systems. To illustrate the proposed method, a model example of finding the distribution of a nonstationary temperature field in a seven-layer flat structure under the influence of the hydrocarbon temperature of the fire is solved. The condition of ideal or non-ideal thermal contact is fulfilled between two adjacent layers. In addition, some layers have internal heat sources. The results of the calculations are presented in the form of a graph of temperature changes depending on timeand spatial coordinates.

Investigation of thermomechanical processes in miniature membrane elastic elements

Purpose: The demand for the devices structures reliability and machines requires understanding elements operation, in particular elastic elements, under the effect of nonstationary temperature factors. Therefore, it is important to investigate the behaviour of these elements under variable temperature effecting. Design/methodology/approach: In this article, the temperature field and the thermal stresses of the membrane type elastic elements, as well as the thermal deformation of its body part were investigated by the method of numerical analysis. The theoretical results have experimental confirmation. Findings: The article shows possibilities significantly reduce the thermal stress in an elastic element, thereby increase its functional and structural reliability by varying the geometric parameters of the elastic element, the materials selection, and body shape. Research limitations/implications: Numerical modelling of thermal processes requires accurate information about the physico-mechanical properties of materials and heat-exchange coefficient, which in practice may differ from the theoretical ones. Therefore, experimental confirmation of research and decisions is needed. The influence of the "hot" thermal shock was investigated. There is performed interest to investigate the "cold" thermal shock. Practical implications: The obtained results allow creating elastic elements with better functional characteristics for operation in a wide temperature range. They can also be used in the designing of elastic elements not only of membrane type. Originality/value: Performed investigation of thermomechanical processes in the membrane elastic element has revealed important features of its temperature deformations with nonstationary thermal influence. Namely, the nature of thermal deformations can be changed by selecting the geometrical parameters of the element, its material, as well as the conditions of heat-exchange conditions with mating member (body). In this way, it is possible to obtain a controlled deformation and to design the elastic elements with predetermined functional tasks. On the other hand, the design of the membrane element body can create elastic hinges, which allows reducing the thermal stress in the membrane, which significantly increases the reliability of the element operation of this type in conditions of non-stationary temperatures. In general, the conducted investigations allow efficient design of elastic elements for devices, sensors and other precision mechanisms.

Nonstationary effects of ocean temperature on Pacific salmon productivity

We tested the hypothesis that ocean temperature effects on productivity for northeast Pacific pink (Oncorhynchus gorbuscha), sockeye (Oncorhynchus nerka), and chum salmon (Oncorhynchus keta) changed after 1988–1989, coincident with a decline in Aleutian Low variance. Nonstationary temperature effects were tested with three different analytical methods (correlation, mixed-effects models, and variable coefficient generalized additive models) applied to spawner–recruit time series from 86 wild runs between Puget Sound and the northern Bering Sea. All three methods supported the hypothesis, with evidence for change in temperature effects that was strongest in the Gulf of Alaska, British Columbia, and Washington and weakest in the Bering Sea. Productivity for all three species showed generally positive responses to ocean temperature in Alaska before 1988–1989, but generally neutral responses after 1988–1989. British Columbia and Washington salmon showed either neutral responses to temperature (pink), negative responses that weakened after 1988–1989 (sockeye), or a switch from neutral to negative responses (chum). We conclude that the inverse response of Alaskan and more southern salmon populations to temperature variability is a time-dependent phenomenon.