scholarly journals Study on thermal conductivity of porous silicon thermal isolation layer based on micro-structure mathematical model

2010 ◽  
Vol 59 (12) ◽  
pp. 8794
Author(s):  
Xu Lu-Jia ◽  
Hu Ming ◽  
Yang Hai-Bo ◽  
Yang Meng-Lin ◽  
Zhang Jie
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Porous Silicon ◽  
Micro Structure ◽  
Thermal Isolation ◽  
Isolation Layer

Design and Simulation of Thermopile Sensor Technology Based on Porous Silicon

2015 ◽  
Vol 741 ◽  
pp. 289-293
Author(s):  
Yan Wei Dou ◽  
Cheng Jun Qiu ◽  
Bo Zang ◽  
Jing Xuan Wang ◽  
Xiao Dong Zhang
Keyword(s):  
Mechanical Property ◽  
Porous Silicon ◽  
Polycrystalline Silicon ◽  
Sensor Technology ◽  
Thermal Isolation ◽  
Thermoelectromotive Force ◽  
Software Analysis ◽  
Ansys Simulation ◽  
Isolation Layer ◽  
Thermopile Sensor

Thermopile sensor using porous silicon (PS) as thermal isolation layer was designed. Thermal stability and mechanical property of sensor were simulated by IntelliSuite CAD software. Analysis results showed stress and temperature distribution of PS layer. Ansys simulation indicated that thermocouple’s thermoelectromotive force was decided by its material composition. If thermocouple was composed of polycrystalline silicon/aluminum, its thermoelectromotive force would reach 256.8 μV/K.

Mathematical model implementation in conditions of uncertainty and possible risks

2021 ◽  
pp. 137-145
Author(s):  
A. Kravtsov ◽  
◽  
D. Levkin ◽  
O. Makarov ◽  
◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Layer Structure ◽  
Boundary Value ◽  
Goal Function ◽  
Cauchy Problems ◽  
System Of Differential Equations

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

scholarly journals Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity

2021 ◽  
Vol 321 ◽  
pp. 03005
Author(s):  
George Kuvyrkin ◽  
Inga Savelyeva ◽  
Daria Kuvshinnikova
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Numerical Solution ◽  
Complex Structure ◽  
Modern World ◽  
Nonlocal Term ◽  
Material Structure ◽  
Two Dimensional ◽  
Differential Heat

Nonlocal models of thermodynamics are becoming more and more popular in the modern world. Such models make it possible to describe materials with a complex structure and unique strength and temperature properties. Models of nonlocal thermodynamics of a continuous medium establish a relationship between micro and macro characteristics of materials. A mathematical model of thermal conductivity in nonlocal media is considered. The model is based on the theory of nonlocal continuum by A.K. Eringen. The interaction of material particles is described using local and nonlocal terms in the law of heat conduction. The nonlocal term describes the effect of decreasing the influence of the surrounding elements of the material structure with increasing distance. The effect of nonlocal influence is described using the standard non-locality function based on the Gaussian distribution. The nonlocality function depends on the distance between the elements of the material structure. The mathematical model of heat conduction in a nonlocal medium consists of an integro-differential heat conduction equation with initial and boundary conditions. A numerical solution to the problem of heat conduction in a nonlocal plate is obtained. The numerical solution of a two-dimensional problem based on the finite element method is described. The influence of nonlocal effects and material parameters on the thermal conductivity in a plate under highintensity surface heating is analyzed. The importance of nonlocal characteristics in modelling the thermodynamic behaviour of materials with a complex structure is demonstrated.

Characterization of a silicon thermal gas-flow sensor with porous silicon thermal isolation

2002 ◽  
Vol 2 (5) ◽  
pp. 463-475 ◽  
Author(s):  
G. Kaltsas ◽  
A.A. Nassiopoulos ◽  
A.G. Nassiopoulou
Keyword(s):  
Porous Silicon ◽  
Gas Flow ◽  
Flow Sensor ◽  
Thermal Isolation

scholarly journals The Non-Stationary Thermal Mode for Barrier Building Constructions in Non-Symmetric Boundary Conditions

2018 ◽  
Vol 7 (3.2) ◽  
pp. 535
Author(s):  
Olena Borshch ◽  
Volodymyr Borshch ◽  
Dmytro Guzyk
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Mathematical Model ◽  
Boundary Conditions ◽  
Thermal Diffusion ◽  
Thermal State ◽  
Thermal Mode ◽  
Temperature Mode ◽  
Deep Layers

In barrier building constructions the heat transfer occurs both at the expense of thermal conductivity and as a result of liquid and air vapors resistance. The mechanism of such resistance differs from classical processes of diffusion and the laws of hydrodynamics for integral medium.The temperature mode of the surface and deep layers of barrier building constructions in non-symmetric boundary conditions was     analyzed. A mathematical model was developed that characterizes the change in the thermal state of barrier constructions during thermal diffusion. The method for calculating the non-stationary thermal modes of flat walls was presented.  

Fabrication of a Microbiochemical Reactor with Thick Thermal Isolation Layer and Integrated Pt Heater/Sensor in the Microwell

2004 ◽  
Vol 43 (6B) ◽  
pp. 3868-3871 ◽  
Author(s):  
Hoon-Sung Choi ◽  
Chang-Taeg Seo ◽  
Duk-Soo Eun ◽  
Jang-Kyoo Shin ◽  
Pyung Choi ◽  
...  
Keyword(s):  
Thermal Isolation ◽  
Isolation Layer

Thermal conductivity modeling of periodic porous silicon with aligned cylindrical pores

2012 ◽  
Vol 111 (12) ◽  
pp. 124329 ◽  
Author(s):  
Tse-Yang Hsieh ◽  
Herng Lin ◽  
Tsang-Jen Hsieh ◽  
Juan-Chen Huang
Keyword(s):  
Thermal Conductivity ◽  
Porous Silicon ◽  
Cylindrical Pores ◽  
Conductivity Modeling

Low-cost flow-rate estimate in separate layers along gas wells from temperature and pressure profiles

2013 ◽  
Vol 53 (1) ◽  
pp. 285
Author(s):  
Emile Barrett ◽  
Imran Abbasy ◽  
Chii-Rong Wu ◽  
Zhenjiang You ◽  
Pavel Bedrikovetsky
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Flow Rate ◽  
Low Cost ◽  
Pressure Sensors ◽  
Gas Wells ◽  
Production Rates ◽  
Pressure Profiles ◽  
Temperature And Pressure ◽  
The Mathematical Model

Estimation of rate profile along the well is important information for reservoir characterisation since it allows distinction of the production rates from different layers. The temperature and pressure sensors in a well are small and inexpensive; while flow meters are cumbersome and expensive, and affect the flow in the well. The method presented in this peer-reviewed paper shows its significance in predicting the gas rate from temperature and pressure data. A mathematical model for pressure and temperature distributions along a gas well has been developed. Temperature and pressure profiles from nine well intervals in field A (Cooper Basin, Australia) have been matched with the mathematical model to determine the flow rates from different layers in the well. The presented model considers the variables as functions of thermal properties at each location, which is more accurate and robust than previous methods. The results of tuning the mathematical model to the field data show good agreement with the model prediction. Simple and robust explicit formulae are derived for the effective estimation of flow rate and thermal conductivity in gas wells. The proposed approach has been applied to determine the well gas rate and formation thermal conductivity from the acquired well pressure and temperature data in field A. It allows for recommending well stimulation of layers with low production rates.

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