Alternating-Direction Implicit Finite-Difference Method for Transient 2D Heat Transfer in a Metal Bar using Finite Difference Method

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Abstract

Different analytical and numerical methods are commonly used to solve transient heat conduction problems. In this problem, the use of Alternating Direct Implicit scheme (ADI) was adopted to solve temperature variation within an infinitesimal long bar of a square cross-section. The bottom right quadrant of the square cross-section of the bar was selected. The surface of the bar was maintained at constant temperature and temperature variation within the bar was evaluated within a time frame. The Laplace equation governing the 2-dimesional heat conduction was solved by iterative schemes as a result of the time variation. The modelled problem using COMSOL-MULTIPHYSICS software validated the result of the ADI analysis. On comparing the Modelled results from COMSOL MULTIPHYSICS and the results from ADI iterative scheme graphically, there was an high level of agreement between both results.
Original languageEnglish
Pages (from-to)105-108
Number of pages4
JournalInternational Journal of Scientific and Engineering Research
Volume6
Issue number6
Publication statusPublished - Jun 2015
Externally publishedYes

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Finite difference method
Heat transfer
Metals
Heat conduction
Laplace equation
Temperature
Numerical methods

Cite this

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title = "Alternating-Direction Implicit Finite-Difference Method for Transient 2D Heat Transfer in a Metal Bar using Finite Difference Method",
abstract = "Different analytical and numerical methods are commonly used to solve transient heat conduction problems. In this problem, the use of Alternating Direct Implicit scheme (ADI) was adopted to solve temperature variation within an infinitesimal long bar of a square cross-section. The bottom right quadrant of the square cross-section of the bar was selected. The surface of the bar was maintained at constant temperature and temperature variation within the bar was evaluated within a time frame. The Laplace equation governing the 2-dimesional heat conduction was solved by iterative schemes as a result of the time variation. The modelled problem using COMSOL-MULTIPHYSICS software validated the result of the ADI analysis. On comparing the Modelled results from COMSOL MULTIPHYSICS and the results from ADI iterative scheme graphically, there was an high level of agreement between both results.",
author = "Ashaju, {Abimbola Ayodeji} and Samson Bright",
year = "2015",
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journal = "International Journal of Scientific and Engineering Research",
issn = "2229-5518",
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T1 - Alternating-Direction Implicit Finite-Difference Method for Transient 2D Heat Transfer in a Metal Bar using Finite Difference Method

AU - Ashaju, Abimbola Ayodeji

AU - Bright, Samson

PY - 2015/6

Y1 - 2015/6

N2 - Different analytical and numerical methods are commonly used to solve transient heat conduction problems. In this problem, the use of Alternating Direct Implicit scheme (ADI) was adopted to solve temperature variation within an infinitesimal long bar of a square cross-section. The bottom right quadrant of the square cross-section of the bar was selected. The surface of the bar was maintained at constant temperature and temperature variation within the bar was evaluated within a time frame. The Laplace equation governing the 2-dimesional heat conduction was solved by iterative schemes as a result of the time variation. The modelled problem using COMSOL-MULTIPHYSICS software validated the result of the ADI analysis. On comparing the Modelled results from COMSOL MULTIPHYSICS and the results from ADI iterative scheme graphically, there was an high level of agreement between both results.

AB - Different analytical and numerical methods are commonly used to solve transient heat conduction problems. In this problem, the use of Alternating Direct Implicit scheme (ADI) was adopted to solve temperature variation within an infinitesimal long bar of a square cross-section. The bottom right quadrant of the square cross-section of the bar was selected. The surface of the bar was maintained at constant temperature and temperature variation within the bar was evaluated within a time frame. The Laplace equation governing the 2-dimesional heat conduction was solved by iterative schemes as a result of the time variation. The modelled problem using COMSOL-MULTIPHYSICS software validated the result of the ADI analysis. On comparing the Modelled results from COMSOL MULTIPHYSICS and the results from ADI iterative scheme graphically, there was an high level of agreement between both results.

M3 - Article

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SP - 105

EP - 108

JO - International Journal of Scientific and Engineering Research

JF - International Journal of Scientific and Engineering Research

SN - 2229-5518

IS - 6

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