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The fourth‐dimention concept in the finite element analysis of transient heat transfer problems
Author(s) -
Chung K. S.
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620170302
Subject(s) - finite element method , heat transfer , thermal conduction , transient (computer programming) , convective heat transfer , dimension (graph theory) , laminar flow , mathematics , domain (mathematical analysis) , steady state (chemistry) , radiative transfer , mechanics , mathematical analysis , physics , computer science , thermodynamics , chemistry , pure mathematics , operating system , quantum mechanics
This study presents the finite element analysis for the transient heat transfer problems by introducing the Fourth‐dimension concept. Time is treated as an additional dimension in the solution domain thereby Increasing the number of dimensions by one. For instance, a three‐dimensional transient problem can be considered as a four‐dimensional problem in the x , y , z , t domain and a two‐dimensional transient problem can be considered as a three‐dimensional steady‐state problem in the x , y , t domain, respectively. The variational principle of the finite element method and the techniques existing for steady‐state problems can be directly utilized. Numerical calculations were performed for heat conduction problems, laminar‐turbulent convective heat transfer problems, and radiative heat transfer problems.