Mathematical Model of the Bridgman-Stockbarger Method to Growth Semiconductor Single Crystals

1992 ◽  
Vol 278 ◽  
Author(s):  
E. Vega ◽  
G. Muiñiz ◽  
F. Rabago
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Single Crystals ◽  
Transfer Equation ◽  
Point System ◽  
Two Dimensional ◽  
Heat Transfer Equation ◽  
Stability Problems ◽  
Stockbarger Method ◽  
Dimensional Equation

AbstractA two dimensional equation has been solved which represents the heat transfer equation for the growth of single crystals system called Bridgman- Stockbarger method. Two variations were analyzed with and without an insulation between heater and cooler. System without an insulation shows stability problems because it's directly affected by the boundary between the cooler and heater region, in this case we obtained a discontinuity in this point. System with an insulation shows higher stability.

Systems Actuated by Shape Memory Alloys: Identification and Modeling

2021 ◽  
Vol 1 (2) ◽  
pp. 12-20
Author(s):  
Najmeh Keshtkar ◽  
Johannes Mersch ◽  
Konrad Katzer ◽  
Felix Lohse ◽  
Lars Natkowski ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Transfer Equation ◽  
Mechanical Parameters ◽  
Heat Transfer Equation ◽  
The Mathematical Model

This paper presents the identification of thermal and mechanical parameters of shape memory alloys by using the heat transfer equation and a constitutive model. The identified parameters are then used to describe the mathematical model of a fiber-elastomer composite embedded with shape memory alloys. To verify the validity of the obtained equations, numerical simulations of the SMA temperature and composite bending are carried out and compared with the experimental results.

Research on Heat Distribution in a Thermal Insulation Space and a Kind of Evaluation Involving Heat-Distribution and Valid Heating-Area

2013 ◽  
Vol 444-445 ◽  
pp. 1427-1433
Author(s):  
Hong Yang Jin ◽  
Zhi Hua Chen ◽  
Lang Li
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Standard Deviation ◽  
Thermal Insulation ◽  
Transfer Equation ◽  
Heating Process ◽  
Heat Distribution ◽  
Heat Transfer Equation ◽  
Heat Transmission

Considering that food always be spoiled in an oven, an analysis of the heat distribution of an object (pan) in a thermal insulation space has been done. The analysis based on the characteristics of heat transmission in an oven. A mathematical model is designed to illustrate the heating process. Specifically, in order to monitor the temperature of the object, pdetool in MATLAB is used to solve the heat transfer equation. Then to evaluate how an object performs in the oven, a method of standard deviation has been introduced. For the efficiency, valid heating area should also be considered. Thus an evaluation is made to choose a most preferring pan, which is balanced between heat distribution and valid heating area (number of pans). The experiment shows that shapes would devote much in performance. It is also demonstrated that there is a certain shape that can be most suitable to be a pan.

scholarly journals MULTICOMPONENT ITERATIVE METHOD FOR SOLVING TWO‐DIMENSIONAL HEAT TRANSFER EQUATION ON MOVING GRIDS

2000 ◽  
Vol 5 (1) ◽  
pp. 164-174
Author(s):  
S. Sytova
Keyword(s):  
Heat Transfer ◽  
Iterative Method ◽  
Transfer Equation ◽  
Nonlinear Parabolic Equations ◽  
Two Dimensional ◽  
Adaptive Grids ◽  
Heat Transfer Equation ◽  
Moving Grids ◽  
Nonlinear Parabolic ◽  
Mixed Derivatives

A multicomponent iterative method of domain decomposition on adaptive grids for solution of two‐dimensional heat transfer equation is proposed. The adaptive grid is constructed in curvilinear space where Cartesian grid is non‐stationary and depends on the solution behavior. In curvilinear space the initial two‐dimensional heat transfer equation is converted to the system of nonlinear parabolic equations with mixed derivatives, a source and convective transfer.

scholarly journals Laplace transform series expansion method for solving the local fractional heat-transfer equation defined on Cantor sets

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 777-780
Author(s):  
Huan Sun ◽  
Xing-Hua Liu
Keyword(s):  
Heat Transfer ◽  
Laplace Transform ◽  
Series Expansion ◽  
Transfer Equation ◽  
Expansion Method ◽  
Cantor Sets ◽  
Heat Transfer Equation ◽  
Local Fractional Calculus ◽  
The Laplace Transform ◽  
Series Expansion Method

In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.

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