Two-Dimensional Heat Transfer Model for Rapid Solidification of Ceramic Alloys

2007 ◽  
Vol 352 ◽  
pp. 13-16
Author(s):  
Zoran S. Nikolic ◽  
Masahiro Yoshimura
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Rapid Solidification ◽  
Difference Method ◽  
Control Volume ◽  
Copper Substrate ◽  
Interface Tracking ◽  
Transfer Model ◽  
Two Dimensional

A finite difference method based on control volume methodology and interface-tracking technique for simulation of rapid solidification accompanied by melt undercooling will be described and applied to analyze the solidification of alumina sample on copper substrate.

scholarly journals Solving of Two-Dimensional Unsteady-State Heat-Transfer Inverse Problem Using Finite Difference Method and Model Prediction Control Method

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Shoubin Wang ◽  
Rui Ni
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Measurement Errors ◽  
Control Method ◽  
Two Dimensional ◽  
Measurement Point ◽  
Prediction Control

The Inverse Heat Conduction Problem (IHCP) refers to the inversion of the internal characteristics or thermal boundary conditions of a heat transfer system by using other known conditions of the system and according to some information that the system can observe. It has been extensively applied in the fields of engineering related to heat-transfer measurement, such as the aerospace, atomic energy technology, mechanical engineering, and metallurgy. The paper adopts Finite Difference Method (FDM) and Model Predictive Control Method (MPCM) to study the inverse problem in the third-type boundary heat-transfer coefficient involved in the two-dimensional unsteady heat conduction system. The residual principle is introduced to estimate the optimized regularization parameter in the model prediction control method, thereby obtaining a more precise inversion result. Finite difference method (FDM) is adopted for direct problem to calculate the temperature value in various time quanta of needed discrete point as well as the temperature field verification by time quantum, while inverse problem discusses the impact of different measurement errors and measurement point positions on the inverse result. As demonstrated by empirical analysis, the proposed method remains highly precise despite the presence of measurement errors or the close distance of measurement point position from the boundary angular point angle.

Eight Surfaces of Radiation Heat Transfer Network Model Development

2013 ◽  
Vol 391 ◽  
pp. 191-195 ◽  
Author(s):  
Ummi Kalthum Ibrahim ◽  
Ruzitah Mohd Salleh ◽  
W. Zhou
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Radiative Heat ◽  
Radiation Heat Transfer ◽  
Model Development ◽  
Transfer Model ◽  
View Factor ◽  
Radiation Heat

This paper deals with the numerical solution for radiative heat transfer within a heated six wall surfaces baking oven, baking tin surface and bread surface. The radiation heat transfer model is constructed by adopting a radiation network representation analysis. The analysis applies view factor and radiosity in determining the radiation rates for each surface in the oven. The amount of radiation heat, q and temperature, T variables are equivalent to electric current and voltage, respectively. Finite difference method coupled with Gauss-Seidel iteration was selected to solve the equations involved in the analysis. Even though this method is tedious and intractable for multiple surfaces, but it would seem to be the most accurate and suitable approach for radiation analysis in the enclosure.

scholarly journals Comparison of the Current Tubes Method with Normal Numerical Methods with the Two-Dimensional Filtration of the Marked Liquid

2018 ◽  
Vol 16 (3) ◽  
pp. 129
Author(s):  
S V Denisov ◽  
V E Lyalin ◽  
R O Sultanov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Control Volume ◽  
Control Surface ◽  
Two Dimensional ◽  
Volume Method

В качестве широко используемого численного метода решения уравнений без учета дисперсионного члена был выбран метод конечных объемов (finite volume method или FVM). В работе представлено введение в суть метода применительно к области гидродинамики и его сравнение с другими численными методами. Метод конечных объемов первоначально развивался как особая формулировка метода конечных разностей (finite difference method или FDM). Показано, что для реализации метода конечных объемов может использоваться базис как метода конечных разностей (FDM), так и метода конечных элементов (finite element method или FEM). Метод конечных объемов использует понятие контрольного объема (control volume или ) и контрольной поверхности (control surface или ), поэтому иногда этот метод называют методом контрольного объема. При этом основное уравнение сохранения записывается в интегральном виде. Далее проводится дискретизация этого уравнения, которая в данном примере будет осуществляться методом конечных разностей (FDM). Показано, что при большом числе трубок тока решение на базе метода трубок тока является точным для случая отсутствия диффузии и может быть использовано для вычисления пространственной ошибки.

HEAT TRANSFER IN LARGE RUBBER ELEMENTS THROUGH OF MODELING BY FINITE DIFFERENCE METHOD

2019 ◽  
Author(s):  
Lucas Peixoto ◽  
Ane Lis Marocki ◽  
Celso Vieira Junior ◽  
Viviana Mariani
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method

A Meshless Finite Difference Method for Conjugate Heat Conduction Problems

2009 ◽  
Author(s):  
Chandrashekhar Varanasi ◽  
Jayathi Y. Murthy ◽  
Sanjay Mathur
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Conjugate Heat Transfer ◽  
Sparse Matrix ◽  
Complex Geometries ◽  
Meshless Finite Difference Method ◽  
Transfer Problems

In recent years, there has been a great deal of interest in developing meshless methods for computational fluid dynamics (CFD) applications. In this paper, a meshless finite difference method is developed for solving conjugate heat transfer problems in complex geometries. Traditional finite difference methods (FDMs) have been restricted to an orthogonal or a body-fitted distribution of points. However, the Taylor series upon which the FDM is based is valid at any location in the neighborhood of the point about which the expansion is carried out. Exploiting this fact, and starting with an unstructured distribution of mesh points, derivatives are evaluated using a weighted least squares procedure. The system of equations that results from this discretization can be represented by a sparse matrix. This system is solved with an algebraic multigrid (AMG) solver. The implementation of Neumann, Dirichlet and mixed boundary conditions within this framework is described, as well as the handling of conjugate heat transfer. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. Metrics for accuracy are provided and future extensions are discussed.

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