Hybrid pseudospectral–finite difference method for solving a 3D heat conduction equation in a submicroscale thin film

2007 ◽  
Vol 23 (5) ◽  
pp. 1139-1148 ◽  
Author(s):  
S.H. Momeni-Masuleh ◽  
A. Malek
Keyword(s):  
Thin Film ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Heat Conduction Equation ◽  
Conduction Equation

Linear Heat Conduction Equation Based Filtering Iteration for Topology Optimization

2012 ◽  
Author(s):  
Qing-hai Zhao ◽  
Xiao-kai Chen ◽  
Yi Lin ◽  
Zheng-Dong Ma
Keyword(s):  
Topology Optimization ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Method ◽  
Heat Conduction Equation ◽  
Neumann Boundary ◽  
Filter Method ◽  
Stability Factor

This paper deals with an alternative approach to density and sensitivity filtering based on the solution of the linear heat conduction equation which is proposed for eliminating checkerboard patterns and mesh dependence in topology optimization problems. In order to guarantee the existence, uniqueness and stability of the solution of PDE, Neumann boundary conditions are introduced. With the help of the existing computational framework of FEM, boundary points have been extended to satisfy Neumann boundary conditions, and together with finite difference method to solve this initial boundary value. In order to guarantee the stability, stability factor is introduced to control the deviation for the solution of the finite difference method. Then the filtering technique is directly applied to the design variables and the design sensitivities, respectively. Especially, different from previous methods based on convolution operation, filtering iteration is employed to ensure the function to eliminate numerical instability. When the value of stability factor is changed at setting range, the number of times of filtering is manually corresponding set. At last, using different test examples in 2D show the advantage and effectiveness of filtering iteration of the new filter method in compared with previous filter 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.

Numerical Modelling of Nanocomposites Using GA and FD Techniques

2019 ◽  
Vol 969 ◽  
pp. 478-483 ◽  
Author(s):  
Siddhartha Kosti ◽  
Jitender Kundu
Keyword(s):  
Genetic Algorithm ◽  
Heat Conduction ◽  
Finite Difference ◽  
Numerical Modelling ◽  
Structural Properties ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Weight Percentage ◽  
Finite Difference Technique ◽  
Finite Difference Techniques

Use of nanocomposites is increasing rapidly due to their enhanced thermal and structural properties. In the present work, the numerical modelling of nanocomposites is conducted with the help of the (GA) genetic algorithm and (FD) finite difference techniques to find out a set of nanocomposites with best thermal and structural properties. The genetic algorithm is utilized to find out the best set of nanocomposites on the basis of thermal and structural properties while the finite difference technique is utilized to solve the heat conduction equation. Different nanocomposites considered in the present work are Al-B4C, Al-SiC and Al-Al2O3. The weight percentage of these nanocomposites is varied to see its effect on the nanocomposites properties. In the end, the solidification curve for all the nanocomposites is plotted and analysed. Result reveals that GA helps in identifying the best set of nanocomposites while FD technique helps in predicting the solidification curve accurately. Increment in the wt. % of nanocomposites makes the solidification curve steeper.

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

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