Thermosensitive Plate Research Articles

Nonstationary Problems of Heat Conduction for a Thermosensitive Plate with Nonlinear Boundary Condition on One Surface

We propose a method for the determination of temperature fields formed in a plate with regard for the thermal radiation, temperature dependence of thermal characteristics, and densities of surface and volumetric heat sources for a nonuniform distribution of the initial temperature. By using the Kirchhoff transformation, Green’s function, generalized functions, and linear splines, we reduce the problems of heat conduction to the solution of a recurrence nonlinear algebraic equation for the values of the Kirchhoff variable at the spline nodes on the corresponding boundary surface. The results of numerical analysis are presented.

Quality assessment of offset thermosensitive printing plates

This article discusses the technological possibilities of assessing the quality of offset thermosensitive printing plates by studying the influence of the structural and physical properties of their construction layers, as well as the parameters of digital computer-to-plate recording on the quality of formation and reproduction of image elements. The article presents an original conceptual model for determining the integral quality indicators of printing plates, taking into account their structural and physical properties, a set of modern methods for evaluating the quality of offset printing forms is presented, such as evaluating the surface morphology of polymer registering layers and a substrate – a basis of the printing form; assessment of the adhesion of polymer layers of offset printing plates to the substrate surface, taking into account the influence of image recording parameters; investigation of the influence of the chemical state of the registering layers of offset plates on the adhesion of printing elements to inks; assessment of the influence of the processes of thermal action of laser radiation and the temperature gradient on the surface structure of the polymer layer of a thermosensitive plate and the accuracy of the formation of the quality of discrete image elements on printing plates.These researches are aimed at determining the relationship between the structural and physicochemical properties of offset thermosensitive plates and integral indicators of the reproduction quality of raster and line image elements in a digital recording system.

Математичні моделі температурного поля в термочутливих елементах електронних пристроїв

Nonlinear mathematical models for the analysis of temperature regimes in a thermosensitive isotropic plate heated by locally concentrated heat sources have been developed. For this purpose, the heat-active zones of the plate are described using the theory of generalized functions. Given this equation of thermal conductivity and boundary conditions contain discontinuous and singular right parts. The original nonlinear equations of thermal conductivity and nonlinear boundary conditions are linearized by Kirchhoff transformation. To solve the obtained boundary value problems, the integral Fourier transform was used and, as a result, their analytical solutions in the images were determined. The inverse integral Fourier transform was applied to these solutions, which made it possible to obtain analytical expressions for determining the Kirchhoff variable. As an example, the linear dependence of the thermal conductivity on temperature is chosen, which is often used in many practical problems. As a result, analytical relations were obtained to determine the temperature in the heat-sensitive plate. The given analytical solutions are presented in the form of improper convergent integrals. According to Newton’s method (three eighths), numerical values of these integrals are obtained with a certain accuracy for given values of plate thickness, spatial coordinates, specific power of heat sources, thermal conductivity of structural materials of the plate and geometric parameters of the heat-active zone. The material of the plate is silicon and germanium. To determine the numerical values of temperature in the structure, as well as the analysis of heat transfer processes in the middle of the plate due to local heating, developed software, using which geometric mapping of temperature distribution depending on spatial coordinates, thermal conductivity, specific heat flux density. The obtained numerical values of temperature testify to the correspondence of the developed mathematical models of the analysis of heat exchange processes in the thermosensitive plate with local heating to the real physical process.

Температурні режими в термочутливих елементах цифрових пристроїв, спричинені локальним нагріванням

Nonlinear mathematical models for the analysis of temperature regimes in a thermosensitive isotropic plate heated by locally concentrated heat sources have been developed. For this purpose, the heat-active zones of the plate are described using the theory of generalized functions. Given this, the equation of thermal conductivity and boundary conditions contain discontinuous and singular right parts. The original nonlinear equations of thermal conductivity and nonlinear boundary conditions are linearized by Kirchhoff transformation. To solve the obtained boundary value problems, the integral Fourier transform was used and, as a result, their analytical solutions in the images were determined. The inverse integral Fourier transform was applied to these solutions, which made it possible to obtain analytical expressions for determining the Kirchhoff variable. As an example, the linear dependence of the thermal conductivity on temperature is chosen, which is often used in many practical problems. As a result, analytical relations were obtained to determine the temperature in the heat-sensitive plate. The given analytical solutions are presented in the form of improper convergent integrals. According to Newtons method (three-eighths), numerical values of these integrals are obtained with a certain accuracy for given values of plate thickness, spatial coordinates, specific power of heat sources, the thermal conductivity of structural materials of the plate, and geometric parameters of the heat-active zone. The material of the plate is silicon and germanium. To determine the numerical values of temperature in the structure, as well as the analysis of heat transfer processes in the middle of the plate due to local heating, developed software, using which geometric mapping of temperature distribution depending on spatial coordinates, thermal conductivity, specific heat flux density. The obtained numerical values of temperature testify to the correspondence of the developed mathematical models of the analysis of heat exchange processes in the thermosensitive plate with local heating to the real physical process. The software also makes it possible to analyze such environments that are exposed to local heat loads in terms of their heat resistance. As a result, it becomes possible to increase it and to protect it from overheating, which can cause the destruction not only of individual elements but also of the entire structure. Keywords: temperature field; isotropic thermosensitive plate; thermal conductivity; heat-insulated surface; perfect thermal contact; local heating.

Construction and a preliminary study of paracrine effect of bone marrow-derived endothelial progenitor cell sheet

The release of paracrine factors from endothelial progenitor cell (EPC) sheet is a central mechanism of tissue repair. The purpose of this study was to constuct the rat bone marrow derived-endothelial progenitor cell (BM-EPCs) sheet and investigate invest the role of stromal cell-derived factor-1α (SDF-1α)/CXCR4 axis in the biological function of BM-EPCs sheet. BM-EPC cells were identified by the cell-surface markers-CD34/CD133/VE-cadherin/KDR using flow cytometry and dual affinity for acLDL and UEA-1. After 7 days of incubation, the BM-EPC single-cell suspensions were seeded on thermo-sensitive plate to harvest the BM-EPC cell sheets. The expression levels of SDF-1α/CXCR4 axis-associated genes and proteins were examined using RT-qPCR and western blot analysis, and enzyme-linked immunosorbent assay (ELISA) was applied to determine the concentration of vascular endothelial growth factor (VEGF), epidermal growth factor (EGF) and SDF-1α in the cell culture medium. The BM-EPC cell sheets were successfully harvested. Moreover, BM-EPC cell sheets have superior migration and tube formation activity when compared with single cell suspension. When capillary-like tube were formed from EPCs sheets, the releasing of paracrine factors such as VEGF, EGF and SDF-1α were increased. To reveal the mechanism of tube formation of BM-EPCs sheets, our research showed that the activation of PI3K/AKT/eNOS pathway was involved in the process, because the phosphorylation of CXCR, PI3K, AKT and eNOS were increased. BM-EPC cell sheets have superior paracrine and tube formation activity than the BM-EPC single-cell. The strong ability to secrete paracrine factors was be potentially related to the SDF-1α/CXCR4 axis through PI3K/AKT/eNOS pathway.

Analytical Solution of the Problem of Symmetric Thermally Stressed State of Thick Plates Based on the 3D Elasticity Theory

An important place among thermoelasticity problems is occupied by the plane elasticity problem obtained from the general three-dimensional problem after using plane stress state hypotheses for thin plates. In the two-dimensional formulation, this problem has become widespread in the study of the effect of temperature loads on the stress state of thin thermosensitive plates. The article proposes a general three-dimensional solution of the static problem of thermoelasticity in a form convenient for practical application. To construct it, a particular solution of the inhomogeneous equation, the thermoelastic displacement potential, was added by us to the general solution of Lamé's equations, the latter solution having been previously found by us in terms of three harmonic functions. It is shown that the use of the proposed solution allows one to satisfy the relation between the static three-dimensional theory of thermoelasticity and boundary conditions, and also to construct a closed system of partial differential equations for the introduced two-dimensional functions without using hypotheses about the plane stress state of a plate. The thermoelastic stress state of a thick or thin plate is divided into two parts. The first part takes into account the thermal effects caused by external heating and internal heat sources, while the second one is determined by a symmetrical force load. The thermoelastic stresses are expressed in terms of deformations and known temperature. A three-dimensional thermoelastic stress-strain state representation is used and the zero boundary conditions on the outer flat surfaces of the plate are precisely satisfied. This allows us to show that the introduced two-dimensional functions will be harmonic. After integrating along the thickness of the plate along the normal to the median surface, normal and shear efforts are expressed in terms of three unknown two-dimensional functions. The three-dimensional stress state of a symmetrically loaded thermosensitive plate was simplified to the two-dimensional state. For this purpose, we used only the hypothesis that the normal stresses perpendicular to the median surface are insignificant in comparison with the longitudinal and transverse ones. Displacements and stresses in the plate are expressed in terms of two two-dimensional harmonic functions and a particular solution, which is determined by a given temperature on the surfaces of the plate. The introduced harmonic functions are determined from the boundary conditions on the side surface of the thick plate. The proposed technique allows the solution of three-dimensional boundary value problems for thick thermosensitive plates to be reduced to a two-dimensional case.

Determination of static thermoelastic state of layered thermosensitive plate, cylinder and sphere

Determination of static thermoelastic state of layered thermosensitive plate, cylinder and sphere

Non-stationary heat conduction problems for thermosensitive plate with nonlinear boundary condition on one of the surfaces

Non-stationary heat conduction problems for thermosensitive plate with nonlinear boundary condition on one of the surfaces

Epicardial Transplantation of Adipose Mesenchymal Stromal Cell Sheets Promotes Epicardial Activation and Stimulates Angiogenesis in Myocardial Infarction (Experimental Study)

Aim: to evaluate the impact of tissue-engineered structures (TES) transplantation based on mesenchymal stromal cell (MSC) sheets in myocardial infarction on the activation of the epicardial cell pool and vascularization of the damaged zone.Materials and methods. Mesenchymal stromal cells were obtained from samples of subcutaneous fat of Wistar rats and C57Bl/6 mice. Tissue engineering structures were obtained by culturing cell sheets on thermosensitive plates (Nunc Dishes with UpCell Surface). Transplantation of TESs was performed after myocardial infarction modeling in rats by ligation of the anterior descending coronary artery. Transplant cells and damaged zones were assessed using immunofluorescent staining of myocardial cryosections. The impact of MSC secretion products on the migration activity of epicardial cells in vitro was evaluated using the explant culture method.Results. MSCs in TESs after transplantation remain viable and induce activation of the epicardial cell pool and local increase of the damaged zone vascularization. The in vitro experiments showed that the conditioned environment of MSCs stimulates the migratory activity of epicardial cells and initiates the formation of activated Wt1/POD1 precursor cells.Conclusion. TES transplantation on the basis of MSC sheets seems to be a promising approach for effective delivery of viable cells into myocardium to activate the epicardial cellular niche and reparative angiogenesis.

Non-stationary heat conduction problems for thermosensitive plates

Determination of the temperature fields in the plates, taking into account the non-uniform distribution of the initial temperature, thermal radiation, temperature dependence of thermophysical characteristics, densities of surface and volume heat sources is reduced to recurrent systems of nonlinear algebraic equations. The Kirchhoff transform, Green's functions of corresponding linear heat conduction problems and linear splines were used. An example of numerical studies is provided. Cite as: B. V. Protsyuk, “Non-stationary heat conduction problems for thermosensitive plates,” Prykl. Probl. Mekh. Mat. , Issue 17, 121–133 (2019) (in Ukrainian), https://doi.org/10.15407/apmm2019.17.121-133

Визначення квазістатичного термопружного стану шаруватих термочутливих плит

The technique of determining the quasistatic thermoelastic state of the layered thermosensitive plates free of load is illustrated. Much attention is paid to finding analytical-numerical solutions of one-dimensional non-stationary heat conduction problems taking into account the temperature dependences of the thermal and temperature conductivity coefficients. Their finding involves use of the Kirchhoff transformation, generalized functions, Green's functions of the corresponding linear heat conduction problem, exact sums of the series, in particular those for which the Gibbs effect takes place, linear splines and solving the received recurrent systems of nonlinear algebraic equations relative to the values in the nodes of the spline of the Kirchhoff variable on the layer division surfaces and the derivative in time on inner flat-parallel surfaces of layers. The results of numerical calculations of temperature fields in two-layer plates with different thicknesses of layers and the external surface heated by a constant heat flux are presented. The accuracy of the found solution is investigated. The comparison of the temperature fields, which are determined assuming simple nonlinearity, stable thermophysical characteristics with the ones based on the exact solution of the corresponding nonlinear stationary heat conduction problem is fulfilled.

INVESTIGATION OF TEMPERATURE MODES IN THERMOSENSITIVE NON-UNIFORM ELEMENTS OF RADIOELECTRONIC DEVICES

Context. The non-linear boundary value problem of heat conduction for a thermosensitive non-homogeneous strip-shaped element of a radio-electronic system with a through inclusion has been solved whose analytical-numerical solution enables us to analyze temperature regimes in the element. Objective. Is to develop such a method of linearization of mathematical model of heat conduction which enables us to obtain analytical numerical solution of the corresponding non-linear boundary value problem for determination of temperature field in elements of radio electronic devices, which are geometrically represented by a thermosensitive plate with a through inclusion. Method. A linearizing function which enables us to partially linearize the initial non-linear mathematical model of heat conduction for a thermosensitive non-homogeneous element of a radio electronic system in the form of “plate-inclusion” structure has been suggested. The introduced piece-wise linear approximation of temperature on plate-inclusion interfaces has enabled us to completely linearize the corresponding partially linearized boundary value problem relative to the linearizing function. After this, it became possible to apply Fourier’s integral transformation to the obtained linear problem with respect to one of the spatial coordinates, as well as to determine the linearizing function. The linear dependence of the coefficient of heat conductivity on temperature for structure materials with the use of the linearizing function has been considered. By solving the boundary value problem, the formulae for determination of temperature field in the “plate-inclusion” thermosensetive structure have been obtained. Results. The obtained formulae for determination of temperature field in a thermosensitive non-homogeneous element of radio electronic system were used to create the software which enables us to obtain distribution of value of temperature and to analyze temperature regimes. Conclusions. A mathematical model for the calculation for the temperature field in a “plate-inclusion” thermosensitive structure is adequate to the actual physical process, because no jump of temperature at “plate-inclusion” interfaces is observed. The numerical results for the chosen materials under linear dependence of the coefficient of thermoconductivity on temperature differ by 7% from the results which are obtained for constant coefficient of heat conductivity. Prospect of further investigation will consider more complicated geometric representation of elements of radio electronic systems.

Modeling and Determination of the Nonsteady Thermoelastic State of a Two-Layer Thermosensitive Plate

On the basis of a model of thermosensitive bodies, we determine the distribution of the unsteady temperature field and the thermoelastic state caused by this field in a two-layer plate. A solution of the nonlinear nonstationary problem of heat conduction is constructed with the use of the Kirchhoff transformation, the method of linearizing parameter, and the integral Laplace transformation with respect to time. The influence of the temperature dependence of the thermophysical and mechanical characteristics of the materials of layers on the values and nature of the distributions of temperature and thermal stresses caused by this dependence in the plate are numerically analyzed.

Static thermoelasticity problems for layered thermosensitive plates with cubic dependence of the coefficients of heat conductivity on temperature

We describe an analytic-numerical method of solution of one-dimensional static thermoelasticity problems for layered plates, heated in different ways. We take into account the cubic dependence of the coefficients of heat conductivity and arbitrary nature of the dependence of other physicomechanical parameters on temperature. Here, using the constructed exact solution of an auxiliary problem, we have reduced the heat conduction problems, irrespective of the number of layers, to the solution of one or a system of two nonlinear algebraic equations. We have also studied the temperature fields and stresses in four-layer plates under conditions of complex heat exchange.

Thermal and Thermoelastic State of Thin-Walled Thermosensitive Structures Subject to Complex Heat Exchange

By the example of determining the temperature field in a half-infinite thermosensitive plate under heat exchange, we illustrate the method of linearizing parameters developed for evaluation of the temperature field in thin-walled structures as well as the stressed-strained state caused by the found temperature distribution.

Stressed state of a thermosensitive plate in a central-symmetric temperature field

The problem of thermoelasticity for a thin thermosensitive plate placed in a central-symmetric temperature field is reduced by the perturbation method to a recurrent sequence of boundary-value problems for differential equations with constant coefficients. On this basis, we obtain solutions for the cases of load-free circular washer, infinite plate with circular hole, circular disk, and infinite plate. The stress-strain state of an infinite plate containing a circular hole is investigated.

Nonlinear heat-conduction problem for an orthotropic thermosensitive plate

We consider the solution of the nonlinear heat-conduction problem for an orthotropic thermosensitive plate heated by a uniformly moving heat source.