Abstract
Heat conduction problem in solid continuum is one of the major fields in mechanics. This chapter presents detail derivations of the finite element matrices of one, two, and three-dimensional conduction problems. Both variational and Galerkin methods are employed to derive the finite element formulations. Derivation of the capacitance matrix for the transient heat conduction problems is carried out for the one, two, and three-dimensional cases.
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References
Wilson EL, Nickell RE (1966) Application of the finite element method to heat conduction analysis. Nuclear Eng Des 4:276–286
Obert EF (1960) Concepts of thermodynamics. McGraw-Hill, New York
Arpaci VS (1966) Conduction heat transfer. Addison, Wesley, Reading
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© 2014 Springer International Publishing Switzerland
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Eslami, M.R. (2014). Conduction Heat Transfer in Solids. In: Finite Elements Methods in Mechanics. Solid Mechanics and Its Applications, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-08037-6_6
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DOI: https://doi.org/10.1007/978-3-319-08037-6_6
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08036-9
Online ISBN: 978-3-319-08037-6
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