An improved finite-difference method for heat- transfer calculations.

1967 ◽  
Vol 4 (4) ◽  
pp. 538-538 ◽  
Author(s):  
SIDNEY GROSS
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method

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.

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>

scholarly journals Application of Finite Difference Method for determining lunar regolith diurnal temperature distribution

2018 ◽  
Vol 49 ◽  
pp. 00052 ◽  
Author(s):  
Marcin Kaczmarzyk ◽  
Marcin Gawronski ◽  
Grzegorz Piatkowski
Keyword(s):  
Heat Transfer ◽  
Heat Flow ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Lunar Regolith ◽  
In Situ Measurements ◽  
Thermal Boundary Conditions ◽  
Transient Heat Flow

This study was performed in order to verify viability of using finite difference method and proposed simple astrometrical model for modelling heat transfer in lunar regolith. The concept was examined by developing FD model of heat flow for upper 0,9 m of lunar regolith, and comparing obtained results with in situ measurements provided by Apollo 15 and 17 heat flow experiments. The model was based on FDM approximation of Fourier’s law for one dimensional transient heat flow. Both constant and temperature-dependent thermophysical properties of lunar regolith were obtained from in situ measurements. Thermal boundary conditions were assumed on in situ measurements and on remote sensing based analytical model. In order to approximate Sun's position at lunar sky, simple analytical astrometric model of lunar rotation was developed. Matlab 2012a was used to conduct the calculations. Stable solutions were obtained for latitudes between 0 and 80°. Satisfactory agreement between Apollo 15 and 17 in situ measurements and FDM modelling was observed. A conclusion was reached, that both FDM and proposed astrometrical model are to be successfully applied for modelling heat transfer in lunar regolith.

Prediction of Tool and Chip Temperature in Continuous Metal Cutting and Milling

2000 ◽  
Author(s):  
Ismail Lazoglu ◽  
Yusuf Altintas
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Contact Zone ◽  
Difference Method ◽  
Metal Cutting ◽  
Transient Temperature ◽  
Time Varying ◽  
First Order ◽  
Chip Temperature

Abstract A finite difference method is presented to predict tool and chip temperature fields in continuous machining and time varying milling processes. Continuous machining operations like orthogonal cutting are studied by modeling the heat transfer between the tool and chip at the contact zone. The shear energy created in the primary zone, the friction energy produced at the rake face - chip contact zone and the heat balance between the moving chip and stationary tool are considered. The temperature distribution is solved using finite difference method. Later, the model is extended to milling where the cutting is interrupted and the chip thickness varies with time. The time varying chip is digitized into small elements with differential cutter rotation angles. The temperature field in each differential element is modeled as a first order dynamic system, whose time constant is identified based on the thermal properties of the tool and work material, and the initial temperature at the previous chip segment. The transient temperature variation is evaluated by recursively solving the first order heat transfer problem at successive chip elements. The proposed model combines the steady-state temperature prediction in continuous machining with transient temperature evaluation in interrupted cutting operations where the chip and the process change in a discontinuous manner. The mathematical models and simulation results are in satisfactory agreement with experimental temperature measurements reported in the literature.

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