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>

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.

scholarly journals Determination of Reservoir Properties of Gas Layers under Conditions of Creep of Rocks with the Kernel of Abel

2021 ◽  
Vol 133 (2) ◽  
pp. 31-33
Author(s):  
B. Z. Kazymov ◽  
◽  
Т. А. Samadov ◽  
S. H. Novruzova ◽  
E. V. Gadashova ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Weighted Average ◽  
Reservoir Properties ◽  
Reservoir Volume ◽  
The Finite Difference Method ◽  
Over Time

The problem of determining reservoir properties (porosity, permeability) of gas layers developed in the depletion mode, whose rocks are subjected to creeping deformation with the Abel core, is considered. In order to determine the parameters that characterize reservoir properties of the reservoir, the authors indicate the possibility of using an appropriate numerical solution to the problem of determining the theoretical values of the reservoir volume-weighted average reservoir pressures over time, obtained using the finite difference method.

A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE’s

2014 ◽  
Vol 6 (5) ◽  
pp. 693-698 ◽  
Author(s):  
Kosuke Abe ◽  
Nobuyuki Higashimori ◽  
Masayoshi Kubo ◽  
Hiroshi Fujiwara ◽  
Yuusuke Iso
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Hyperbolic Partial Differential Equations ◽  
View Point ◽  
Rounding Errors ◽  
The Finite Difference Method

AbstractThe Courant-Friedrichs-Lewy condition (The CFL condition) is appeared in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. We give a remark on the CFL condition from a view point of stability, and we give some numerical experiments which show instability of numerical solutions even under the CFL condition. We give a mathematical model for rounding errors in order to explain the instability.

scholarly journals Mathematical modeling of air duct heater using the finite difference method

2011 ◽  
Vol 13 (4) ◽  
pp. 47-52
Author(s):  
M. Sarafraz ◽  
S. Peyghambarzadeh ◽  
A. Marahel
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Transfer Coefficients ◽  
Design And Optimization ◽  
The Finite Difference Method

Mathematical modeling of air duct heater using the finite difference method In this research, mathematical modeling of a duct heater has been performed using energy conservation law, Stefan-Boltzman law in thermal radiation, Fourier's law in conduction heat transfer, and Newton's law of cooling in convection heat transfer. The duct was divided to some elements with equal length. Each element has been studied separately and air physical properties in each element have been used based on its temperature. The derived equations have been solved using the finite difference method and consequently air temperature, internal and external temperatures of the wall, internal and external convection heat transfer coefficients, and the quantity of heat transferred have been calculated in each element and effects of the variation of heat transfer parameters have been surveyed. The results of modelling presented in this paper can be used for the design and optimization of heat exchangers.

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