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Research Papers: Conduction

Modification of the Classical Boundary Integral Equation for Two-Dimensional Transient Heat Conduction With Internal Heat Source, With the Use of NURBS for Boundary Modeling

[+] Author and Article Information
Eugeniusz Zieniuk

Faculty of Mathematics and Computer Science,
University of Bialystok,
Białystok 15-089, Poland
e-mail: ezieniuk@ii.uwb.edu.pl

Dominik Sawicki

Faculty of Mechanical Engineering,
Bialystok University of Technology,
Białystok 15-089, Poland
e-mail: sawicki.dominik1@gmail.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 18, 2016; final manuscript received February 27, 2017; published online April 19, 2017. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 139(8), 081301 (Apr 19, 2017) (11 pages) Paper No: HT-16-1215; doi: 10.1115/1.4036099 History: Received April 18, 2016; Revised February 27, 2017

The most popular methods used for solving transient heat conduction problems, like finite element method (FEM) and boundary element method (BEM), require discretization of the domain or the boundary. The discretization problem escalates for unsteady issues, because an iterative process is required to solve them. An alternative to avoid the mentioned problem is parametric integral equations systems (PIESs), which do not require classical discretization of the boundary and the domain, while being numerically solved. PIES have been previously used with success to solve steady-state problems. Moreover, they have been recently tested also with success for transient heat conduction problems, without internal heat sources. The purpose of this paper is to generalize PIES based on analytical modification of classical boundary integral equation (BIE) for transient heat conduction with internal heat source and nonuniform rational basis spline (NURBS) for boundary modeling. The obtained generalization of PIES is tested on examples, mostly with defined exact solution.

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Figures

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Fig. 1

The considered rectangular domain with boundary conditions

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Fig. 2

L2 norm of temperature error in time, for ten points located on one of the boundary segments, compared to FEM

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Fig. 3

L2 norm of temperature error in time, for 50 points located inside of the domain, compared to FEM

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Fig. 4

L2 norm of temperature error in time, for ten points located on one of the boundary segments, compared to the exact solution

Grahic Jump Location
Fig. 5

L2 norm of temperature error in time, for 50 points located inside of the domain, compared to the exact solution

Grahic Jump Location
Fig. 6

L2 norm of temperature error in time, for ten points located on one of the boundary segments, compared to the exact solution

Grahic Jump Location
Fig. 7

L2 norm of temperature error in time, for 50 points located inside of the domain, compared to the exact solution

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