Using Excel to Implement the Finite Difference Method for 2-D Heat Transfer in a Mechanical Engineering Technology Course

Abstract: 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 Keywords: heat transfer, triangle coordinates system. Abstrak 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 Kata kunci : perpindahan panas, sistem koordinat segitiga.

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Mathematical modeling of air duct heater using the finite difference method

Polish Journal of Chemical Technology ◽

10.2478/v10026-011-0048-z ◽

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

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-06-2013-0198 ◽

2014 ◽

Vol 24 (8) ◽

pp. 1954-1978 ◽

Cited By ~ 34

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.

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Numerical study of heat transfer in laminar film boiling by the finite-difference method

International Journal of Heat and Mass Transfer ◽

10.1016/0017-9310(84)90239-4 ◽

1984 ◽

Vol 27 (1) ◽

pp. 77-84 ◽

Cited By ~ 10

Author(s):

J. Srinivasan ◽

N.S. Rao

Keyword(s):

Heat Transfer ◽

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Numerical Study ◽

Film Boiling ◽

Laminar Film ◽

The Finite Difference Method

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Numerical Simulation by FDM of Unsteady Heat Transfer in Cylindrical Coordinates

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.851.322 ◽

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.

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A Software Tool for Determining Steady-State Temperature Distributions in a Square Domain by the Finite-Difference Method

International Journal of Mechanical Engineering Education ◽

10.7227/ijmee.35.4.5 ◽

2007 ◽

Vol 35 (4) ◽

pp. 305-315

Author(s):

K. A. Oladejo ◽

D. A. Adetan ◽

O. A. Bamiro

Keyword(s):

Heat Transfer ◽

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Computer Aided Design ◽

Linear Equations ◽

Analytical Techniques ◽

Software Tool ◽

Transfer Equations ◽

The Finite Difference Method

This paper presents the development of an interactive program (called SSTDD) to solve two-dimensional conduction heat transfer equations in a square domain using the finite-difference method. The development of the tool (based on a computer-aided design package), on a Visual BASIC 6.0 platform, involved the application of the heat transfer equations and the appropriate boundary conditions to a square domain. The finite-difference method was used to express the elliptic differential equation in a form suitable for numerical solution. The system of linear equations generated was solved by the Gauss–Seidel iterative technique. The SSTDD model was tested by using problems solved by conventional analytical techniques. The results generated by the model and the analytical method were in good agreement. Hence the model can be used to solve practical engineering problems, with good accuracy, and also as a demonstration tool to students in the area of design and heat transfer of mechanical engineering.

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Modeling and Solving Problems of Heat Transfer of Cement Clinker

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.361-363.1557 ◽

2011 ◽

Vol 361-363 ◽

pp. 1557-1562

Author(s):

Yan Wen ◽

Na Li ◽

Bin Liu

Keyword(s):

Heat Transfer ◽

Porous Media ◽

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Control Model ◽

Cement Clinker ◽

Heat Transfer Characteristics ◽

Heat Transfer Theory ◽

The Finite Difference Method

Based on the analysis of heat transfer characteristics of the cement clinker, the porous media’s seepage heat transfer theory is introduced into researching of clinker heat transfer according to its porous media characteristics, and then the control model of cement clinker is built up. Furthermore, this project solves the model by using the finite difference method. At last, the inherent heat transfer law of cement clinker is obtained through simulation.

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