scholarly journals Universality of one-dimensional heat conductivity

2006 ◽  
Vol 73 (6) ◽  
Author(s):  
Trieu Mai ◽  
Onuttom Narayan
2021 ◽  
Vol 63 (7) ◽  
pp. 975
Author(s):  
А.П. Клинов ◽  
М.А. Мазо ◽  
В.В. Смирнов

The thermal conductivity of a one-dimensional chain of rotators with a double-barrier interaction potential of nearest neighbors has been studied numerically. We show that the height of the "internal" barrier, which separates topologically nonequivalent degenerate states, significantly affects the temperature dependence of the heat conductivity of the system. The small height of this barrier leads to the dominant contribution of the non-linear normal modes at low temperatures. In such a case the coefficient of thermal conductivity turns out to be the risen function of the temperature. The growth of the coefficient is limited by local fluctuations corresponding to jumps over the barriers. At higher values of the internal barrier height, dependence of the heat conductivity on temperature is similar to that of classical rotators.


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Cletus Matthew Magoda ◽  
Jasson Gryzagoridis ◽  
Kant Kanyarusoke

Purpose The purpose of this paper is to validate an assumption of what to use as an effective (steady state) heat transfer coefficient of thermal conductivity for the honeycomb core sandwiched by Fiberglass face sheets composite. A one-dimensional model based on Fourier law is developed. The results are validated experimentally. Design/methodology/approach The results were obtained from the one-dimensional mathematical model of an overall or effective heat conductivity of the Honeycomb composite panel. These results were validated experimentally by applying heat flux on the specimen under controlled environment. The surface temperatures at different voltages were recorded and analysed. The skin of the sandwich composite material used in the investigation was Fiberglass sheet with a thickness of 0.5 mm at the bottom and 1.0 mm at the top surface. Both skins have a stacking sequence of zero degrees. Due to the presence of air cells in the core (Honeycomb), the model considers the conduction, convection and radiation heat transfer, across the thickness of the panel, combined as an effective conduction mode, whose value may be predicted by using the coefficient of thermal conductivity of the air based on the average temperature difference between the two skins. The experimental results for the heat transfer through the thickness of the panel provide validation of this assumption/prediction. Both infrared thermography and conventional temperature measurement techniques (thermocouples) were used to collect the data. Findings The heat transfer experiment and mathematical modeling were conducted. The data obtained were analyzed, and it was found that the effective thermal conductivity was temperature-dependent as expected. The effective thermal conductivity of the honeycomb panel was close to that of air, and its value could be predicted if the panel surface temperatures were known. It was also found that as temperature raised the variation between experimental and predicted effective air conduction raised up. This is because there was an increase in molecular diffusion and vibration. Therefore, the convection heat transfer increased at high temperatures and the air became an insulator. Originality/value Honeycomb composite panels have excellent physical and thermal properties that influence their performance. This study provides an appropriate method in determining thermal conductivity, which is one of the critical thermal properties of porous composite material. This paper also gives useful and practical data to industries that use or manufacture honeycomb composite panels.


2008 ◽  
Vol 22 (22) ◽  
pp. 3901-3914 ◽  
Author(s):  
JUN-WEN MAO ◽  
YOU-QUAN LI ◽  
LING-YUN DENG

We investigate the heat conduction in a modified Lorentz gas with freely rotating disks periodically placed along one-dimensional channel. The heat conductivity is dependent on the moment of inertia η of the disks, with a power-law decay when η > 1. By plotting the Poincaré surface of the section, we observe a contraction of phase space over the range of η > 1, which is sensitive to the initial condition. We find that the power-law decay of the heat conductivity is relevant to the mixing phase space. As a possible application, we model the heterostructure by connecting the segments of different η, and predict the analytical results of the temperature profiles and the heat conductivity, which are in good agreement with the numerical ones.


The structure of one-dimensional flames is shown to be completely determined by constants such as those of heat conductivity, of diffusion, and of the homogeneous reaction rates. The mathematical problem in the most general case is intractable, but three simple cases are solved fully by a mathematical method of successive approximations. The three cases are those in which diffusion is neglected compared with heat conductivity and in which reaction velocities of the following types are considered: unimolecular, bimolecular, and the quasibimolecular form of a unimolecular reaction at low pressures. The method of mathematical approximation is shown to involve errors of the order of only 10 % in some actual cases, an error which is negligible compared with other uncertainties of the problem. In these simple cases it is possible to solve all details of the structure such as the variation of composition and temperature through the flame.


2005 ◽  
Vol 71 (6) ◽  
Author(s):  
Jun-Wen Mao ◽  
You-Quan Li ◽  
Yong-Yun Ji

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