Transient non-linear heat conduction-radiation problems - A boundary element formulation

International Journal for Numerical Methods in Engineering

Volumn 46, Issue 11, 1999, Pages 1865-1882

  Blobner, Jutta ^a   Białecki, Ryszard A ^b   Kuhn, Günther ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Dual reciprocity boundary element method; Heat conduction; Heat radiation; Non linear boundary condition; Non linear material; Transient temperature

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; HEAT CONDUCTION; HEAT FLUX; HEAT RADIATION; INTEGRAL EQUATIONS; LINEARIZATION; ORDINARY DIFFERENTIAL EQUATIONS; RUNGE KUTTA METHODS;

KIRCHHOFF'S TRANSFORMATION;

BOUNDARY ELEMENT METHOD;

BOUNDARY ELEMENT METHOD; HEAT CONDUCTION; HEAT RADIATION;

EID: 0343776199     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19991220)46:11<1865::AID-NME748>3.0.CO;2-D     Document Type: Article

References (21)

1. Białecki RA. Coupled radiative, convective and conductive heat transfer; BEM solution. In Proceedings of IUTAM/IABEM Seminar on non-linear Problems in BEM, Morino L, Wendland L (eds). Kluwer: Dordrecht, 1997; 23-27.
2. Brebbia CA, Telles JFC, Wrobel LC. Boundary Element Techniques: Theory and Applications in Engineering. Springer: Berlin and New York, 1984.
3. Kikuta M, Togoh H, Tanaka M. Boundary element analysis of non-linear transient heat conduction problems. Computer Methods in Applied Mechanics and Engineering 1987; 62:321-329.
4. Partridge PW, Brebbia CA, Wrobel LC. The Dual Reciprocity Boundary Element Method. Computational Mechanics Publications: Southampton and Boston, 1992.
5. Wrobel LC, Brebbia CA. The Dual Reciprocity Boundary Element formulation for non-linear diffusion problems. Computer Methods in Applied Mechanics and Engineering 1987; 65:147-164.
6. Wrobel LC, Brebbia CA. Boundary elements for non-linear heat conduction. Communication in Applied Numerical Methods 1987; 4:617-622.
7. Białecki RA, Nowak AJ. Some remarks on transformation techniques for transient non-linear problems. Engineering Analysis with Boundary Elements 1990; 7:145-146.
8. Brebbia CA, Nowak AJ. Solving heat transfer problems by the Dual Reciprocity BEM. In Boundary Element Methods in Heat Transfer, Wrobel LC, Brebbia CA (eds). Computational Mechanics Publications: Southampton and Boston, 1992; 1-31.
9. Białecki RA. Solving non-linear heat transfer problems using the Boundary Element Method. In Boundary Element Methods in Heat Transfer, Wrobel LC, Brebbia CA (eds). Computational Mechanics Publications: Southampton and Boston, 1992; 87-121.
10. Białecki RA, Nowak AJ, Boundary value problems in heat conduction with non-linear material and non-linear boundary conditions. Applied Mathematical Modelling 1981; 5:417-421.
11. Blobner J, Białecki RA, Kuhn G, Transient conduction-radiation problems; Dual reciprocity solution. In Proceedings of the 20th World Conference on the Boundary Element Method (BEM20), Brebbia CA, Kassab A. (eds). Computational Mechanics Publications: Southampton and Boston, 1998; 627-636.
12. Bialecki RA. Solving Heat Radiation Problems Using the Boundary Element Method. Computational Mechanics Publications: Southampton and Boston, 1993.
13. Białecki RA, Grela Ł. Practical aspects of developing heat radiation BEM code. In Proceedings of the 9th International Conference on Boundary Element Technology, Brebbia CA, Kassab A (eds). Computational Mechanics Publications, Southampton and Boston, 1994; 29-39.
14. Golberg MA, Chen CS. The theory of radial basis functions applied to BEM for inhomogeneous partial differential equations. Boundary Element Communication 1994; 5:57-61.
15. Bialecki RA, Merkel M, Mews H, Kuhn G. In- and out-of-core BEM equation solver with parallel and non-linear options. International Journal for Numerical Methods in Engineering 1996; 39:4215-4242.
16. Zienkiewicz OC, Taylor RL. The Finite Element Method (4th edn). McGraw-Hill: London, 1989.
17. Eisner N. Grundlagen der Technischen Thermodynamik (3rd edn). Vieweg: Braunschweig, 1982.
18. Pina HLG, Fernandes JLM. Applications in Transient Heat Conduction. In Topics in Boundary Element Research, Brebbia CA (ed.). Springer: Berlin, 1984; 41-58.
19. Consigny H, Richards BE. Short duration measurements of heat transfer rate to a gas turbine rotor blade. Journal of Engineering for Power, Transactions ASME 1982; 104:542-551.
20. Gröber H, Erk S, Grigull U. Die Grundgesetze der Wärmeübertragung (3rd edn). Springer: Berlin, 1981.
21. Touloukian YS, Kirby RK, Taylor RE, Desai PD. Thermophysical properties of matter. Purdue Research Foundation: New York, 1970.