Nonstationary Heat Research Articles

Adaptive step size controllers based on Runge-Kutta and linear-neighbor methods for solving the non-stationary heat conduction equation

<abstract><p>We systematically test families of explicit adaptive step size controllers for solving the diffusion or heat equation. After discretizing the space variables as in the conventional method of lines, we are left with a system of ordinary differential equations (ODEs). Different methods for estimating the local error and techniques for changing the step size when solving a system of ODEs were suggested previously by researchers. In this paper, those local error estimators and techniques are used to generate different types of adaptive step size controllers. Those controllers are applied to a system of ODEs resulting from discretizing diffusion equations. The performances of the controllers were compared in the cases of three different experiments. The first and the second system are heat conduction in homogeneous and inhomogeneous media, while the third one contains a moving heat source that can correspond to a welding process.</p></abstract>

Конечно-элементное моделирование нестационарных задач теплопроводности при сложном теплообмене

The article presents a numerical simulation of nonstationary heat conduction problems under complex heat transfer, which includes such heat transfer mechanisms as heat conduction, convection, and radiation. The Stefan-Boltzmann law describes the resulting heat transfer by radiation between two bodies, where the heat transfer coefficient is a function of the body surface temperature. An algorithm and software for solving the heat conduction problem using the finite element method were developed, and the influence of external impacts on the temperature field distribution in the vicinity of an insulated circular hole in the center of the body was studied. The temperature fields were investigated for various boundary conditions in the hole of the plate and the corresponding isotherms were given.

Cooling of an infinite rectangular plate with an adibatically insulated side

The work is devoted to the issues of non-stationary heat transfer. The article presents a solution for the distribution of the temperature field in an infinite rectangular plate with an adiabatically isolated side. As a result, an analytical expression of the plate temperature distribution is obtained in the form of a series containing trigonometric and exponential functions. The paper also considered special cases when the internal thermal resistance of thermal conductivity is greater and when the external resistance of heat output is less. Special cases were interpreted physically. One of the special cases leads the problem to a problem with boundary conditions of the first kind, when the surface temperature is constant, which indicates the reliability of the results obtained.

Нестаціонарний теплообмін — визначення коефіцієнта тепловіддачі стаціонарним методом та методом регулярного теплового режиму

Нестаціонарний теплообмін — визначення коефіцієнта тепловіддачі стаціонарним методом та методом регулярного теплового режиму

Numerical calculation of heat transfer in a multilayer composite structure with honeycomb filler during autoclave molding at the heating stage

The production of any multilayer structure begins with the development of technological documentation, which describes, among other things, the temperature regimes during their manufacture. Conventionally, the temperature process of polymerization can be divided into three stages: preheating, temperature stabilization and cooling. The paper presents the results of a numerical calculation of temperature fields in a multilayer composite structure with a honeycomb filler during its manufacture by autoclave molding at the preheating stage. This method of manufacturing composite structures makes it possible to mold parts of varying complexity and dimensions, the demand for which is growing in such industries as mechanical engineering, aircraft building, and shipbuilding. The requirements for the quality of such products are increasing, which is greatly influenced by compliance with the temperature regime during molding. Conducting direct experiments requires large energy costs, therefore, to solve the problem of controlling heat exchange processes inside the structure, mathematical models were developed that describe these processes. A non-stationary heat conduction problem is formulated for a multilayer unbounded plate with a constant initial distribution, boundary conditions of the third kind on the outer boundaries, and boundary conditions of the fourth kind on the contact surfaces of the layers. Using the finite element method, the problem is reduced to three-point difference equations, the solution of which is found by the sweep method. The determination of the sweep coefficients is shown taking into account the thermal characteristics of the layers. The results of a numerical calculation of the temperature distribution for a nine-layer composite structure with a honeycomb core are presented. The numerical calculation was carried out using the developed program in the BorlandDelphi 7.0 object-oriented programming environment. The results obtained are presented in the form of graphic dependences of the temperature over the thickness of the sample at different points in time, as well as the dependence of temperature on time at various nodes of the sample in comparison with the theoretical curve. An analysis of these dependences was carried out, which showed that the heating of the sample occurs unevenly over its thickness. The deviation from the theoretical temperature values is observed in the layers located closer to the honeycomb layer. This can adversely affect the course of the polymerization step, which is characterized by the conversion of the binder into a polymer, and occurs at certain temperatures. Therefore, achieving the desired temperature values at the stage of heating the structure is important for the manufacture of reliable and durable structures that can withstand extreme operating conditions. The obtained temperature distributions make it possible to correct the technological process of manufacturing various multilayer structures at the stage of its development, which will reduce the economic costs of production.

The behavior of heat transfer and entropy in a thin layer of liquid under laser heating

Experimental studies of heat flux, Nusselt number, heat transfer coefficient and entropy generation under local laser heating in the range of water layer heights from 1.4 to 5 mm have been carried out. The laser heats a graphite spot on the glass wall, which warms up the liquid. To date, most studies in the fields of the velocity rotor and entropy generation have been carried out theoretically, and in the absence of surface Marangoni forces. There is extremely little experimental data on the measurement of these fields, especially at non-stationary three-dimensional heat exchange. The temperature field on the free surface of the liquid layer is strongly inhomogeneous and asymmetrical at a layer height of 1.4 mm. At a layer height of 4–5 mm, the symmetry of the temperature field increases. Using the optical method of Particle Image Velocimetry, instantaneous fields of velocity and vorticity have been studied. As the layer height increases, the characteristic size of vortex structures on the liquid surface rapidly decreases with a sharp decrease in the correlation function of the vortex flow. Local laser heating of the layer creates a spatially uneven heat exchange, which is formed during self-organization of various convective vortex structures. For the first time it is shown that the behavior of entropy generation during local heating of the layer differs from the case with uniform heating of the wall. The transition of a symmetric velocity field from two vortices to an asymmetric field with many vortices leads to a decrease in entropy generation with an increase in the Rayleigh and Marangoni numbers. The heat transfer coefficient in the liquid decreases with increasing layer height from 1.4 mm to 5 mm.

Differential-difference model of heat transfer in solids using the method of parametric identification

The paper considers the problem of parametric identification of a differential-difference model of the heat transfer process in a spherical body. When developing the model, the original extended Kalman filter is used which allows taking into account the dependence of the thermophysical properties of the object under study on temperature. This formulation and the obtained solution of the problem make it possible to take into account the different nature of the external thermal effect and the processes occurring inside the bodies, in particular, during phase transitions in systems of bodies. The research results obtained using parametric identification and Ansys software are in good agreement. However, the method we have considered, in contrast to the Ansys software, allows not only to determine the temperature at different points of the object, but also to restore the non-stationary heat flow at the object boundary as well as to refine its thermophysical properties. The considered method of parametric identification of the differential-difference model of heat transfer can be successfully used in determining the efficiency of heat energy storage devices.

Effects of Joule annealing on the magnetoimpedance characteristics of Nb-doped Co-based metallic microfibers

The microstructure and magnetic properties of Co-based metallic microfibers before and after Joule annealing were comprehensively investigated to enhance the magnetoimpedance (MI) effect of metallic microfibers and facilitate the development of magnetic sensor applications. In particular, high-resolution transmission electron microscopy was used to investigate the microstructural changes induced by Joule annealing and to, further elucidate the associated mechanism. The experimental results show that the microfibers have a smooth and homogeneous surface, with no apparent macro/micro defects, as well as high glass-forming ability and thermal stability. Additionally, the 90 mA-annealed microfibers exhibit good magnetic properties, and their M s , M r , H c , and μ m are 81.40 emu/g, 15.01 emu/g, 33.63 Oe, and 0.1471 nm, respectively. The 90 mA-annealed microfibers also exhibit excellent MI performance. Accordingly, the [Δ Z/Z max ] max and ξ max are 213.08% and 41.76%/Oe as f = 1 MHz, respectively. Therefore, the Joule annealing treatment can significantly improve the MI properties of Co-based metallic microfibers, providing technical support for the development of sensitive materials for high-performance MI sensors. The transient temperature rising characteristic of Nb-doped Co-based metallic microfibers during Joule annealing can be numerically calculated based on a non-stationary heat conduction model, further to obtain the optimum parameters of practical annealing process. Accordingly, the MI properties of metallic microfibers were enhanced especially at the current intensity of 90 mA. Furthermore, Joule annealing could effectively eliminate the residual inner stress and improve the atomic short-range ordering arrangement, and the current could generate a stably toroidal magnetic field, which further regulates the toroidal distribution of magnetic domain structure, thereby improves the circumferential permeability, magnetic anisotropy field and MI properties.

Registration of Nonstationary Heat Flux Dynamics in Shock Tunnels Using High-Speed Thermography

Registration of Nonstationary Heat Flux Dynamics in Shock Tunnels Using High-Speed Thermography

Study of heating kinetics and temperature fields of melon fruits under IR irradiation

This article is devoted to the study of heating kinetics, temperature fields, as well as determining the laws of non-stationary heat transfer processes during treatment of melon fruits with IR rays. These studies, in turn, make it possible to determine the heating time to the desired temperature under different radiation conditions, which is a necessary condition for achieving a positive effect of heat treatment in infrared radiation. At the same time, the study of temperature fields and heating kinetics is carried out in order to reach the optimal regime obtained in the treatment of melon fruits with IR rays as a result of planning the experiment. The optimization of the process shows that the most appropriate mode of heat treatment of melon fruits during drying is IR irradiation at an incident flux density of 23-24 kW/m2 in a pulsed mode: τ=95 (-40)+60 (-30)+60 sec. The analysis of heating kinetics and temperature field confirms the correct selection of the optimal modes obtained in controlling the process of treatment of melon fruits with IR rays and allows to establish the laws of heat-mass transfer.

Conjugate Nonstationary Heat Transfer in the Course of Supersonic Spatial Flow Past a Spherically Blunted Cone Made from a Combined Material

Conjugate Nonstationary Heat Transfer in the Course of Supersonic Spatial Flow Past a Spherically Blunted Cone Made from a Combined Material

A Phase-Field Approach to Continuum Damage Mechanics.

This paper develops a phase-field approach to describe the damage within continuum mechanics. The body is associated with the standard stresses and body forces of macroscopic character. As is the case in many contexts, the phase field is a scalar variable whose time rate is governed by a constitutive equation. The generality of the approach allows the modeling of non-stationary heat conduction, mechanical hysteretic effects, and the macroscopic damage. The thermodynamic consistency is investigated through the constraint of the Clausius-Duhem inequality following the standard procedure of Rational Thermodynamics. The entropy production is considered as a constitutive function; this view was proved to be essential in the elaboration of hysteretic models. Here, the scheme is improved by viewing the entropy production as a sum of two terms, one induced by the other constitutive equations and one given by a constitutive equation of the entropy production per se.

Nonstationary Complex Heat Transfer Problem in a System of Grey Bodies with Semitransparent Inclusions

Nonstationary Complex Heat Transfer Problem in a System of Grey Bodies with Semitransparent Inclusions

Heat transfer under high-power heat release: Not fully stable fluids as potential heat carriers

• Significant disturbance in heat transfer under high-power heating was detected. • Supercritical-pressure water and highly unstable aqueous mixture were studied objects. • Heat transfer deterioration stage preceding macroscopic phase transition was revealed. • This stage is assumed to have universal character for fluid phase transitions. • Its nature is associated with the violation of homogeneity of not fully stable system. In this paper, we present new data on non-stationary heat transfer in sub- and supercritical liquids due to high-power heat release in a wire probe immersed in an investigated liquid. In the performed experiments, the characteristic heating time was from 5 to 180 ms, while the corresponding thickness of the heated layer was in the magnitude order of 10 1 µm. The impetus for the study came from the previous discovery of two unexpected effects. The first was a deterioration of heat transfer during the rapid transition of a compressed fluid to the supercritical region of temperatures along the isobar. The second was the distinctive character of the change in the heat flux density of a binary, partially miscible liquid when going deeper into the region of its unstable states. The study is aimed at clarifying the prospects of using supercritical fluids and mixtures with lower critical solution temperatures as potential heat carriers in processes where the possibility of powerful local heat release cannot be excluded.

Full statistics of nonstationary heat transfer in the Kipnis–Marchioro–Presutti model

We investigate non-stationary heat transfer in the Kipnis–Marchioro–Presutti (KMP) lattice gas model at long times in one dimension when starting from a localized heat distribution. At large scales this initial condition can be described as a delta-function, u(x, t = 0) = Wδ(x). We characterize the process by the heat transferred to the right of a specified point x = X by time T, and study the full probability distribution . The particular case of X = 0 has been recently solved by Bettelheim et al (2022 Phys. Rev. Lett. 128 130602). At fixed J, the distribution as a function of X and T has the same long-time dynamical scaling properties as the position of a tracer in a single-file diffusion. Here we evaluate by exploiting the recently uncovered complete integrability of the equations of the macroscopic fluctuation theory (MFT) for the KMP model and using the Zakharov–Shabat inverse scattering method. We also discuss asymptotics of which we extract from the exact solution and also obtain by applying two different perturbation methods directly to the MFT equations.

The Non-Stationary Heat Transport inside a Shafted Screw Conveyor Filled with Homogeneous Biomass Heated Electrically

The non-stationary heat transfer inside a cylindrical channel of a shafted screw conveyor, electrically heated, and filled with a moving biomass was analyzed. The problem of non-stationary heat transport is encountered in the processes of biomass pyrolysis and food products’ sterilization. To solve the heat conduction equation with initial and boundary conditions, the methods of the expansion of the given and unknown functions into a Fourier series in the angular coordinate, and Fourier and Laplace integral transforms in the axial coordinate and time, respectively, were used. As a result of solving this problem, it is shown that the temperature in the reactor consists of two main terms. The first of them is proportional to time, and the second is a superposition of quasi-monochromatic heat pulses decaying with time. Numerical analysis of the temperature distribution in space and time depending on various specific parameters of the system was carried out. The obtained numerical results were compared with those corresponding to the cases of heat sources in the form of a spiral or a shaftless helical screw.

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.

Solution of Inverse Problem of Non-Stationary Heat Conduction Using a Laplace Transform

This paper presents some solutions to the one-dimensional Cauchy-type transient inverse heat conduction problem. Based on known courses of temperature and the heat flux on one of the boundaries of the region, courses of temperature and heat flux on the opposite boundary of the region were determined with the use of the Laplace’s transform. Solution of the inverse problem does not require determination of temperature distribution on subsequent time moments inside the region. Stability of the solution to the inverse problem of the Cauchy type was investigated by means of determining the minimal time step ensuring the stability of the solution. Two examples of one-dimensional transient inverse problems were solved. The first one is related to the reconstruction of shock temperature change on the boundary of the region based on known courses of temperature and heat flux on the opposite boundary. The second one concerned the reconstruction of the heat flux acting on one of the boundaries through a period of time. In both considered problems the reconstructed boundary conditions were discontinuous. Stable results were obtained for both investigated examples, however, the stability of the inverse problem depended on the length of time step.

To the possibility of experimental estimation of the diffusion spinodal position of binary mixture with LCST via pulsed heating method

In this paper, we present new data on non-stationary heating of a platinum wire probe, immersed in a binary partially-miscible liquid. A pressure value and a mass fraction of the a polymer in the mixture were the experimental parameters. The characteristic heating time was from 5 to 15 ms. The object of the research was the water/polypropylene glycol-425 (PPG-425) mixture having lower critical solution temperature (LCST). The position of the diffusion spinodal was estimated based on the obtained data on the liquid-liquid binodal in the framework of the Flory-Huggins approximation. An experimental technique to estimate the position of the spinodal of two-component mixtures with LCST on the scale of the mixture component ratio was developed. It was shown that the method of isobaric pulse heating can be used for this purpose. This representation is based on the threshold change in the heat transfer pattern when crossing the phase coexistence curve and the diffusion spinodal.

Forced Vibrations and Nonstationary Heating of a Rectangular Viscoelastic Plate with Prestresses*

Forced Vibrations and Nonstationary Heating of a Rectangular Viscoelastic Plate with Prestresses*