zbMATH — the first resource for mathematics

Two-dimensional unsteady heat conduction analysis with heat generation by triple-reciprocity BEM. (English) Zbl 0985.80008
Summary: If the initial temperature is assumed to be constant, a domain integral is not needed to solve unsteady heat conduction problems without heat generation using the Boundary Element Method (BEM). However, with heat generation or a non-uniform initial temperature distribution, the domain integral is necessary. This paper demonstrates that two-dimensional problems of unsteady heat conduction with heat generation and a non-uniform initial temperature distribution can be solved approximately without the domain integral by the triple-reciprocity boundary element method. In this method, heat generation and the initial temperature distribution are interpolated using the boundary integral equation.

80M15 Boundary element methods applied to problems in thermodynamics and heat transfer
Full Text: DOI
[1] Nowak, Engineering Analysis with Boundary Elements 6 pp 164– (1989)
[2] In Advanced Formulations in Boundary Element Methods. Chapter 3, (eds). CMP: UK, 1993; 77-115.
[3] The Multiple Reciprocity Boundary Element Method. Computational Mechanics Publication: Southampton, Boston, 1994. · Zbl 0868.73006
[4] In The Multiple Reciprocity Method of Solving Transient Heat Conduction Problems, Advances in Boundary Elements, vol. 2, (eds). Computational Mechanics Publication: Southampton, Springer: Berlin, 1989; 81-93.
[5] Ochiai, Journal of Thermal Stresses pp 397– (1994)
[6] Ochiai, JSME International Journal, Series A 37 pp 355– (1994)
[7] Boundary element method for thermal stresses analysis using cells of boundary type. Proceedings of the First International Symposium on Thermal Stresses and Related Topics, Hamamatsu, 1995; 27-30.
[8] Ochiai, Engineering Analysis with Boundary Elements 18 pp 111– (1996)
[9] Ochiai, Journal of Thermal Stresses 18 pp 603– (1995)
[10] Ochiai, Heat Transfer-Japanese Research 23 pp 498– (1995)
[11] Ochiai, Engineering Analysis with Boundary Elements 23 pp 167– (1999) · Zbl 0940.74076
[12] Boundary Element Techniques?Theory and Applications in Engineering. Springer: Berlin, 1984; 47-107.
[13] Ochiai, Advances in Engineering Software 22 pp 113– (1995) · Zbl 05478751
[14] Ochiai, JSME International Journal 39 pp 93– (1996)
[15] Ochiai, Computer Aided Geometric Design 17 pp 233– (2000) · Zbl 0939.68151
[16] Interpolation of scattered data by radial functions. In Topics in Multivariate Approximation, (eds). Academic Press: London, 1987; 47-61.
[17] Micchelli, Constructive Approximation 2 pp 12– (1986) · Zbl 0625.41005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.