Abstract
Conduction problems amenable to analytical solution have been considered in Chaps. 1–6. These have included both steady and transient conduction in one or more dimensions and in three different coordinate systems. In the present chapter we discuss commonly employed numerical methods for the solution of problems not amenable to exact analysis. Emphasis is on the finite difference method. However it is possible to use other methods such as the finite volume and finite element methods to solve conduction problems. The reader may refer to advanced texts for these methods.
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Notes
- 1.
D.W. Peaceman and H.H. Rachford, The numerical solution of parabolic and elliptic differential equations, SIAM, Vol. 3, pp. 28–41, 1955; see interesting note in SIAM News, Vol. 39, No. 2, March 2006.
- 2.
J. Douglas Jr. and J.E. Gunn, A general formulation of alternate direction methods—part i. parabolic and hyperbolic problems, Numerische Mathematik, Vol. 6, pp. 428–453, 1964.
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Venkateshan, S.P. (2021). Numerical Solution of Conduction Problems. In: Heat Transfer . Springer, Cham. https://doi.org/10.1007/978-3-030-58338-5_7
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DOI: https://doi.org/10.1007/978-3-030-58338-5_7
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