scholarly journals On Solving Problems of Thermal Conductivity on an Anisotropic Plane with a Weakly Permeable Film

2021 ◽  
Vol 16 (3) ◽  
pp. 115-121
Author(s):  
Kholodovskii Svyatoslav Ye. ◽  
◽  
Orlov Aleksey O. ◽  
Keyword(s):  
Thermal Conductivity ◽  
Cauchy Problem ◽  
Initial Temperature ◽  
Practical Interest ◽  
Heat Propagation ◽  
Heat Sources ◽  
Fibrous Materials ◽  
Isotropic Plane ◽  
Fourier Expansions ◽  
Convolution Of Fourier Expansions

The problem of thermal conductivity on an anisotropic plane (x; y) divided into two halfplanes D1(1 < x < 0; y 2 R) and D2(0 < x < 1; y 2 R) by a weakly permeable film x = 0 is considered at given heat sources and a given initial temperature. The anisotropy ellipses are arbitrary (in magnitude and direction) and are the same at all points of the plane. Using the method of convolution of Fourier expansions, the solution of the problem is expressed in single quadratures through the well-known solution of the classical Cauchy problem on an isotropic plane without a film. The results obtained are of practical interest in the problems of heat propagation and conservation in materials with anisotropic properties (crystalline, fibrous materials), in the presence of a thermal insulation film.

scholarly journals Thermal Conductivity, Heat Sources and Temperature Profiles of Li-Ion Batteries

2014 ◽  
Vol 58 (48) ◽  
pp. 145-171 ◽  
Author(s):  
O. S. Burheim ◽  
M. A. Onsrud ◽  
J. G. Pharoah ◽  
F. Vullum-Bruer ◽  
P. J. S. Vie
Keyword(s):  
Thermal Conductivity ◽  
Temperature Profiles ◽  
Heat Sources ◽  
Li Ion Batteries ◽  
Li Ion

COMPUTATIONAL AND EXPERIMENTAL STUDY OF THE EFFECTIVE THERMAL CONDUCTIVITY OF FIBROUS MATERIALS

2021 ◽  
pp. 95-102
Author(s):  
N.N. Vorobev ◽  
◽  
D.Ya. Barinov ◽  
A.V. Zuev ◽  
S.I. Pakhomkin ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Experimental Study ◽  
Heat Flow ◽  
Porous Structure ◽  
Effective Thermal Conductivity ◽  
Fibrous Materials ◽  
Zone Method ◽  
Factors Influencing ◽  
Main Factors ◽  
Hot Zone

The article is devoted to the evaluation of the effect of porosity on the effective thermal conductivity of thermal insulation materials. The main factors influencing the thermal conductivity of the material, such as density, the type of porous structure of the material and humidity, are considered. The method of measuring the thermal conductivity by the stationary heat flow method and the hot zone method is described. A method for calculating the effective thermal conductivity of fibrous materials is presented. A computational and experimental study of the effective thermal conductivity is carried out and the results are analyzed.

A Non-Steady-State Method of Measuring the Thermal Conductivity of Transparent Liquids

1967 ◽  
Vol 22 (7) ◽  
pp. 1005-1011 ◽  
Author(s):  
Silas E. Gustafsson
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Simple Expression ◽  
Optical Path ◽  
Metal Foil ◽  
Heat Sources ◽  
Plane Source ◽  
Average Deviation ◽  
Steady State Method ◽  
The Times

A plane source method has been developed for non-steady-state measurements of the thermal conductivity of transparent liquids. The plane source is realized by using an electrically heated metal foil, suspended in the liquid. The temperature distribution is described by using the concept of instantaneous heat sources giving a simple expression of the optical path, which is recorded with wave-front-shearing interferometry. The thermal diffusivity is determined simply by measuring the positions of the fringes, locating the points where the gradient of the optical path is constant and knowing the times between two subsequent exposures. The accuracy of the method, which is an absolute one, is demonstrated. The average deviation from the recommended values of the thermal conductivity was found to be 0.37%.

Hybrid Thermal Behavior from Thermoelectrics to Heat Sinking of a Thin Si Membrane with Stretched Ge Quantum Dots

2010 ◽  
Vol 1267 ◽  
Author(s):  
Jean-Numa Gillet
Keyword(s):  
Thermal Conductivity ◽  
Quantum Dots ◽  
Thermal Behavior ◽  
Heat Propagation ◽  
Peltier Effect ◽  
Orthogonal Direction ◽  
Thermal Insulating ◽  
Anisotropic Thermal Conductivity ◽  
Ge Quantum Dots ◽  
Heat Sinking

AbstractA membranous nanomaterial showing, for the first time, a hybrid thermal behavior between insulating and dissipative regimes is proposed with applications in both thermoelectrics (low thermal conductivity) and passive heat sinking (high thermal conductivity). While other compounds could be chosen, the nanomaterial is made up of a thin Si membrane covered by Ge quantum dots (QDs) with epitaxial facets. The QDs are voluntarily stretched in the direction [010] or y parallel to the membrane to form elongated islands. The broken symmetry induces an exalted phonon wave-guiding in y. Therefore, when hot and cold junctions are connected to the membrane following the stretching direction [010], the anisotropic thermal conductivity shows a significant exaltation with respect to the in-plane orthogonal direction [100] or x, where the Ge islands have the smallest average size. An example nanomaterial is obtained by repetition of molecular supercell slabs containing 4348 atoms each. The thermal conductivity shows a marked exaltation higher than 22 folds, from 1.5 to 33.5 W/m/K when the connection direction between the hot and cold junctions is rotated by 90° from x to y. Therefore, the nanomaterial presents a changing thermal behavior from insulation to passive dissipation when the heat propagation direction is modified from x to y. As a result, it could be used for the design of passive heat sinkers (from the phonons) when the two junctions are connected following [010]. In contrast, a thermal insulating behavior appears when the junctions are linked following [100]. This direction can be as well used for cooling applications. However, in this case, cooling is differently generated using the Peltier effect (from the electrons). Seebeck generation can be also envisioned in the direction [100].

Thermal Property Measurements of Reactive Materials: The Macroscopic Behavior of a Nanocomposite

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Amanda Gordon ◽  
Keerti Kappagantula ◽  
Michelle L. Pantoya
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Initial Temperature ◽  
Weighted Average ◽  
Laser Flash ◽  
Fuel Particle ◽  
Experimental Measurements ◽  
Weighted Averages ◽  
Reactive Materials ◽  
The Matrix

This study experimentally examined the thermal properties of reactive materials that are a composite of fuel and oxidizer particles. Three reactive materials were selected: aluminum (Al) with iron (III) oxide (Fe2O3); Al with Teflon (C2F4); and Al with titanium (IV) oxide (TiO2). The experimental measurements were performed using a laser flash analyzer (LFA) and then compared with calculations based on weighted averages of each component in the composite. The effects of fuel particle size, oxidizer, and initial temperature on thermal properties were studied. Nanometric Al composites are more insulative than their micron-scale counterparts, exhibiting three times lower thermal conductivity in some cases. Increased overall contact resistance may be a key contributor to the reduction in thermal conductivity. The measured values deviated as high as 69% from weighted average estimates of thermal properties. These results suggest that factors not accounted for in weighted average estimates significantly influence the thermal properties of the matrix.

A Study on Storing Process of Thermoforming Using Finite Difference Method

2011 ◽  
Vol 314-316 ◽  
pp. 571-575
Author(s):  
Zhen Zhe Li ◽  
Gui Ying Shen ◽  
Xiao Qian Wang ◽  
Mei Qin Li ◽  
Yun De Shen
Keyword(s):  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Finite Difference Method ◽  
Initial Temperature ◽  
Thickness Distribution ◽  
Time Dependent ◽  
Maximum Temperature ◽  
Uniform Thickness ◽  
Maximum Temperature Difference

Obtaining a uniform thickness of the final product using thermoforming is difficult, and the thickness distribution depends strongly on the distribution of the sheet temperature. In this paper, the time-dependent temperature distribution of the total sheets in the storing process was studied because the temperature after the storing process is the initial temperature of the preheating process. An analysis code for simulating the storing process was developed under the condition that the thermal conductivity caused by contact resistance between sheets was assumed as a large value. In this study, the number of sheets in the storing room was adjusted for finding out the effect of it. The analysis results show that maximum temperature difference between sheets was significantly different when adjusting the number of sheets in the storing room. The temperature distribution of the total sheets and the method for analysis in this study will be used to optimize the storing process for higher quality of final products.

scholarly journals Numerical investigation of the Carleman system

Vestnik MGSU ◽  
2015 ◽  
pp. 7-15
Author(s):  
Ol’ga Aleksandrovna Vasil’eva
Keyword(s):  
Cauchy Problem ◽  
Equilibrium State ◽  
Numerical Investigation ◽  
Initial Conditions ◽  
Practical Interest ◽  
Statistical Characteristics ◽  
Stabilization Time ◽  
System Solution ◽  
Stochastic Solution ◽  
The Cauchy Problem

In the article the Cauchy problem of the Carleman equation is considered. The Carleman system of equations is a model problem of the kinetic theory of gases. It is a discrete kinetic model of one-dimensional gas consisting of identical monatomic molecules. The molecules can have one of two speeds, which have equal values and opposite directions. This system of the equations is quasi-linear hyperbolic system of partial differential equations. There is no analytic solution for this problem in general case. So, the numerical investigation of the Cauchy problem of the Carleman system solution is very important.The paper presents and discusses the results of the numerical investigation of the Cauchy problem for the studied system solution with periodic initial conditions. The dependence of the stabilization time of the solution and the time dependence of energy exchange from small parameter are obtained.The second point of the paper is numerical investigation of the solution of the Cauchy problem with non-periodic initial conditions. The solution stabilization to the equilibrium state is obtained. The solution stabilization time is compared with stabilization time in periodic case.The final point of the paper is numerical investigation of the Cauchy problem with stationary normal processes as initial conditions. The solution to this problem is two stationary stochastic processes for any fixed value of time variable. As a rule, the practical interest is not a stochastic solution but its statistical characteristics. The stochastic solution realization is presented and discussed. The dependence of the mathematical expectation of the solution deviation modulus from equilibrium state is obtained. It demonstrates the process of the solution stabilization.

scholarly journals CONCEPTION QUASIDERIVATIVES IN THE PROBLEMS OF MATHEMATICAL MODELING OF HEAT TRANSFER

2020 ◽  
Vol 21 ◽  
pp. 79-85
Author(s):  
R. Tatsii ◽  
M. Stasiyk ◽  
O. Pazen ◽  
L. Shypot
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Closed Form ◽  
Critical Radius ◽  
Internal Heat ◽  
Heat Sources ◽  
Internal Heat Sources

In this paper, in closed form, the problems of determining stationary temperature fields in multilayer (flat, cylindrical and spherical) structures in the presence of discrete-continuous internal and point heat sources are solved. The one-dimensional differential equation of thermal conductivity in different coordinate systems is given through one parametric family of quasi-differential equations. It is assumed that the coefficients of the differential equation of thermal conductivity are piecewise constant functions. A system of two linearly independent boundary conditions is added to the equation, which in the general case are nonlocal. The solutions of such problems are constructive and are expressed exclusively through their initial data. The basic provisions of the concept of quasi-derivatives, the provisions of the theory of heat transfer, the theory of generalized systems of linear differential equations, elements of the theory of generalized functions are used. For the mathematical model of stationary thermal conductivity, the practical use of the concept of quasi-derivatives is illustrated, for the efficient construction, in a closed form, of solutions of boundary value problems with the most general boundary conditions. As an example, the problem of finding the critical radii of thermal insulation of multilayer hollow cylinders and spheres, taking into account the internal heat sources in the layers. Boundary conditions of the first and third kind. It is established that the value of the critical radius does not depend on the number of layers and the intensity of internal heat sources, but only on the thermal conductivity of the outer layer of the structure and the heat transfer coefficient between the structure and the environment. The formula for determining the critical radius of thermal insulation for a multilayer cylindrical and spherical structure is derived. The methods developed in this work have the prospect of further development and can be used in engineering calculations.

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

Fire Safety ◽  
2020 ◽  
Vol 36 ◽  
pp. 115-120
Author(s):  
R. Tatsii ◽  
M. Stasiuk ◽  
O. Pazen
Keyword(s):  
Thermal Conductivity ◽  
Heat Exchange ◽  
Thermal Contact ◽  
Internal Heat ◽  
Nonstationary Temperature ◽  
Heat Sources ◽  
Conductivity Equation ◽  
Flat Structure ◽  
Temperature Changes ◽  
Internal Heat Sources

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.

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