Method of Lines to Solve 2-D Steady Temperature Field of FGM

2007 ◽  
Vol 353-358 ◽  
pp. 2003-2006 ◽  
Author(s):  
Wei Tan ◽  
Chang Qing Sun ◽  
Chun Fang Xue ◽  
Yao Dai
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Transfer Problem ◽  
Method Of Lines ◽  
Main Idea ◽  
Functionally Graded ◽  
Temperature Fields ◽  
Steady Temperature ◽  
Thermal Transfer ◽  
Steady Temperature Field

Method of Lines (MOLs) is introduced to solve 2-Dimension steady temperature field of functionally graded materials (FGMs). The main idea of the method is to semi–discretized the governing equation of thermal transfer problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs with functions of thermal properties. As numerical examples, six kinds of material thermal conductivity functions, i.e. three kinds of polynomial functions, an exponent function, a logarithmic function, and a sine function are selected to simulate spatial thermal conductivity profile in FGMs respectively. The steady-state temperature fields of 2-D thermal transfer problem are analyzed by the MOLs. Numerical results show that different material thermal conductivity function has obvious different effect on the temperature field.

Method of Lines to Solve the Linear Temperature Field of LENS

2015 ◽  
Vol 1120-1121 ◽  
pp. 1441-1445
Author(s):  
Chun Fang Xue
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Transfer Problem ◽  
Method Of Lines ◽  
Main Idea ◽  
Functionally Graded ◽  
Temperature Fields ◽  
Linear Temperature ◽  
Steady Temperature Field ◽  
Net Shaping

This article introduces a semi-analytical numerical method ——method of lines(MOLs) to solve steady temperature field of Laser Engineered Net shaping (LENS). The main idea of MOLs is to semi-discretized the governing equation of thermal transfer problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The steady linear temperature fields of functionally graded materials were obtained using MOLs and the regularities of different temperature functions were also found. The effects of thermal conductivity coefficient under different formal functions on thermal temperature fields were analys. Numerical results showed that different material thermal conductivity function had obvious different effect on the temperature field.

Analysis on Steady Temperature of Honeycomb-Core Panel Based on Coupled Aerothermal Heating and Honeycomb Conduction

2011 ◽  
Vol 217-218 ◽  
pp. 1197-1201
Author(s):  
Wei Liang ◽  
Yu Fu ◽  
Zhen Qi Liu ◽  
Lu Lu Yang ◽  
Han Chao Mai
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Numerical Method ◽  
Physical Model ◽  
Thermal Conduction ◽  
Honeycomb Structure ◽  
Honeycomb Core ◽  
Steady Temperature ◽  
Equivalent Thermal Conductivity ◽  
Steady Temperature Field

A physical model is formulated to evaluate the steady temperature field of honeycomb-core panel. The model takes into account the coupled effect of aerothermal heating and radiate energy from front and rear plate and honeycomb thermal conduction. The equations that are established based on the model are solved in numerical method and the equivalent thermal conductivity is obtained. The model is also used to investigate the effect of coming fluid and the geometric parameters of honeycomb structure on the TPS capacity.

Nonlinear Steady Temperature Fields in Non—Homogeneous Materials

2007 ◽  
Vol 561-565 ◽  
pp. 1957-1960
Author(s):  
Yao Dai ◽  
Qi Sun ◽  
Wei Tan ◽  
Chang Qing Sun
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Method Of Lines ◽  
Variable Coefficients ◽  
Temperature Fields ◽  
Gradient Material ◽  
Original Form ◽  
Steady Temperature ◽  
Heat Shielding ◽  
Parameter Values

Functionally gradient material (FGM) developed for heat-shielding structure is often used in the very high temperature environment. Therefore, the material property parameters are not only functions of spatial coordinates but also ones of temperature. The former leads to partial differential equations with variable coefficients, the latter to nonlinear governing equations. It is usually very difficult to obtain the analytical solution to such thermal conduction problems of FGMs. If the finite element method is adopted, it is very inconvenient because material parameter values must be imputed for each element. Hence, a semi-analytic numerical method, i.e., method of lines (MOLs) is introduced. The thermal conductivity functions do not need to be discretized and remain original form in ordinary differential equations. As a numerical example, the nonlinear steady temperature fields are computed for a rectangular non-homogeneous region with the first, the second and the third kinds of boundary conditions, where three kinds of functions, i.e. power, exponential and logarithmic ones are adopted for the thermal conductivity. Results display the important influence of non-linearity on temperature fields. Moreover, the results given here provide the better basis for thermal stress analysis of non-homogenous and non-linear materials.

scholarly journals Impact of Tunnel Temperature Variations on Surrounding Rocks in Cold Regions

2019 ◽  
Author(s):  
Qingyang Yu ◽  
Chao Zhang ◽  
Zhenxue Dai ◽  
Chao Du ◽  
Mohamad Reza Soltanian ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Insulation Layer ◽  
Cold Regions ◽  
Ambient Temperatures ◽  
Temperature Conditions ◽  
Layer Control

Temperature is an important factor in designing and maintaining tunnels, especially in cold regions. We present three-dimensional numerical simulations of tunnel temperature fields at different temperature conditions. We study the tunnel temperature field in two different conditions with relatively low and high ambient temperatures representing winter and summer of northeast China. We specifically study how these temperature conditions affect tunnel temperature and its migration to surrounding rocks. We show how placing an insulation layer could affect the temperature distribution within and around tunnels. Our results show that the temperature field without using an insulation layer is closer to the air temperature in the tunnel, and that the insulation layer has shielding effects and could plays an important role in preventing temperature migration to surrounding rocks. We further analyzed how thermal conductivity and thickness of insulation layer control the temperature distribution. The thermal conductivity and thickness of insulation layer only affect the temperature of the surrounding rocks which are located at distances below ~20 m from the lining.

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