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Applicability Extent of 2-D Heat Equation for Numerical Analysis of a Multiphysics Problem

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https://hdl.handle.net/10037/10351
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article.pdf (438.9Kb)
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article.pdf (320.8Kb)
publisher's pdf (PDF)
Dato
2017-01
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Forfatter
Khawaja, Hassan Abbas
Sammendrag
This work focuses on thermal problems, solvable using the heat equation. The fundamental question being answered here is: what are the limits of the dimensions that will allow a 3-D thermal problem to be accurately modelled using a 2-D Heat Equation? The presented work solves 2-D and 3-D heat equations using the Finite Difference Method, also known as the Forward-Time Central-Space (FTCS) method, in MATLAB®. For this study, a cuboidal shape domain with a square cross-section is assumed. The boundary conditions are set such that there is a constant temperature at its center and outside its boundaries. The 2-D and 3-D heat equations are solved in a time dimension to develop a steady state temperature profile. The method is tested for its stability using the Courant-Friedrichs-Lewy (CFL) criteria. The results are compared by varying the thickness of the 3-D domain. The maximum error is calculated, and recommendations are given on the applicability of the 2-D heat equation.
Beskrivelse
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. Source: http://dx.doi.org/10.1063/1.4972667.
Forlag
American Institute of Physics
Sitering
AIP Conference Proceedings 1798, 020075 (2017)
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