Numerical Simulation by FDM of Unsteady Heat Transfer in Cylindrical Coordinates

2016 ◽  
Vol 851 ◽  
pp. 322-325
Author(s):  
Cláudia Narumi Takayama Mori ◽  
Estaner Claro Romão
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Exact Solutions ◽  
Difference Method ◽  
Transfer Problem ◽  
Cylindrical Coordinates ◽  
Unsteady Heat Transfer ◽  
The Finite Difference Method

In this paper the heat transfer problem in transient and cylindrical coordinates will be solved by the Crank-Nicolson method in conjunction the Finite Difference Method. To validate the formulation will study the numerical efficiency by comparisons of numerical results compared with two exact solutions.

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>

Numerical Simulation of Heat Transfer in a Closed Two-Phase Thermosiphon

2017 ◽  
Vol 743 ◽  
pp. 449-453
Author(s):  
Vladimir Arkhipov ◽  
Alexander Nee ◽  
Lily Valieva
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Phase Transitions ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Mathematical Modelling ◽  
Three Dimensional ◽  
Two Phase ◽  
One Dimensional ◽  
The Finite Difference Method

This paper presents the results of mathematical modelling of three–dimensional heat transfer in a closed two-phase thermosyphon taking into account phase transitions. Three-dimensional conduction equation was solved by means of the finite difference method (FDM). Locally one-dimensional scheme of Samarskiy was used to approximate the differential equations. The effect of the thermosyphon height and temperature of its bottom lid on the temperature difference in the vapor section was shown.

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.

Natural convection inside a C-shaped nanofluid-filled enclosure with localized heat sources

2014 ◽  
Vol 24 (8) ◽  
pp. 1954-1978 ◽  
Author(s):  
M.A. Mansour ◽  
M.A. Bakeir ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Volume Fraction ◽  
Cu Nanoparticles ◽  
Content Type ◽  
The Finite Difference Method

Purpose – The purpose of this paper is to investigate natural convection fluid flow and heat transfer inside C-shaped enclosures filled with Cu-Water nanofluid numerically using the finite difference method. Design/methodology/approach – In this investigation, the finite difference method is employed to solve the governing equations with the boundary conditions. Central difference quotients were used to approximate the second derivatives in both the X and Y directions. Then, the obtained discretized equations are solved using a Gauss-Seidel iteration technique. Findings – It was found from the obtained results that the mean Nusselt number increased with increase in Rayleigh number and volume fraction of Cu nanoparticles regardless aspect ratio of the enclosure. Moreover the obtained results showed that the rate of heat transfer increased with decreasing the aspect ratio of the cavity. Also, it was found that the rate of heat transfer increased with increase in nanoparticles volume fraction. Also at low Rayleigh numbers, the effect of Cu nanoparticles on enhancement of heat transfer for narrow enclosures was more than that for wide enclosures. Originality/value – This paper is relatively original for considering C-shaped cavity with nanofluids.

Numerical Simulation of Consolidation Test Considering Different Drainage Height

2012 ◽  
Vol 170-173 ◽  
pp. 2325-2328
Author(s):  
Yang Liu ◽  
Zhe Wang
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Soil Sample ◽  
Difference Method ◽  
Simulation Method ◽  
Test Apparatus ◽  
Consolidation Test ◽  
Simulation Results ◽  
The Finite Difference Method

Numerical simulation of the consolidation test was developed in different drainage conditions using the finite difference method. Soil sample was divided into layers to determine the time-steps of the test. A series of simulation tests were carried out to study the influence of drainage height on the coefficient ratio. Finally, some experiments data were compared with the numerical simulation results. Numerical results indicate that the simulation method broke through the limitation of test apparatus, and made it possible to conduct big size specimen consolidation test under certain conditions.

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