Generalized Boundary Integral Equation for Transient Heat Conduction in Heterogeneous Media

1998 ◽  
Vol 12 (3) ◽  
pp. 364-373 ◽  
Author(s):  
Eduardo Divo ◽  
Alain Kassab
Keyword(s):  
Integral Equation ◽  
Heat Conduction ◽  
Boundary Integral Equation ◽  
Heterogeneous Media ◽  
Transient Heat Conduction ◽  
Boundary Integral

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

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Eugeniusz Zieniuk ◽  
Dominik Sawicki
Keyword(s):  
Integral Equation ◽  
Heat Conduction ◽  
Heat Source ◽  
Boundary Integral Equation ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Transient Heat Conduction ◽  
Boundary Integral ◽  
Classical Boundary ◽  
Element Method

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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