Comparison of boundary collocation methods for singular and non-singular axisymmetric heat transfer problems

Ramachandran, P.A.; Gunjal, Prashant R.

doi:10.1016/j.enganabound.2008.09.010

Cited by 9 publications

(3 citation statements)

References 31 publications

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“…For Eq. (24), set N = 3, to solve simultaneous equations with 16 different border discrete points in the surface of the ball given. Table 2 gives the analytical solutions and semi-analytical solution with different radius.…”

Section: Electrical Power and Energy Systemsmentioning

confidence: 99%

Collocation Trefftz Method for the Heat Conduction Issue in Irregular Domain

Fan

Zhang

2012

AMR

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Rules for non-orthogonal borders of irregular domain is the thorny issues when using analytical method for solving mathematical and physical equations. On the basis of solution in the form of separated variables, the border of arbitrary shape with non-orthogonal boundary will be separated into a limited number of discrete points, and then direct assignment for the form solution at each of the discrete points on the border according to boundary conditions, at every discrete points on the border can establish an equation. If the number of discrete points on the border is the same with truncated series after retained series, all coefficients of the form solution can be determined and the problem solved. This paper use Laplace equation as an example to illustrate Collocation Trefftz Method can solve certain steady-state heat conduction problems within non-orthogonal border and irregular domain.

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Section: Electrical Power and Energy Systemsmentioning

confidence: 99%

Collocation Trefftz Method for the Heat Conduction Issue in Irregular Domain

Fan

Zhang

2012

AMR

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“…This has lead to the phenomenon of "Interface effect", which makes it difficult to control the interface shape [26,27]. Singularities have also been observed near the triple point in the Czochralski process [28,29]. Asymptotic analysis have found the order of these singularities to be dependant on the angle prescribed by the triple point or the facet corners [30,31].…”

Section: Introductionmentioning

confidence: 99%

Weak Stefan Formulation for Bulk Crystal Growth with Non-smooth Interfaces

Noronha¹,

Ydstie²

2021

Preprint

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Most heat transfer models for bulk crystal growth rely on the classical Stefan formulation to evaluate interface motion during phase change. However, when the interface is non-smooth the use of the classical Stefan formulation may lead to singularities. To address this problem, we propose a simulation model based on the weak formulation of the Stefan problem. Numerical solutions of the weak Stefan formulation are obtained using the finite volume method. This approach provides an energy conserving discretization scheme that accurately evaluates heat transfer around non-smooth interfaces. We apply the weak formulation to numerically simulate the solidification of silicon in the horizontal ribbon growth process. Results exhibit a limitation on the ribbon's pull speed, which previous classical Stefan models have failed to demonstrate. A comparison of heat transfer between radiation and gas cooling shows that gas cooling increases the pull speed limit for the same amount of heat removed.

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“…Applications of BCM for the analysis of plates and shells can be found in the paper by Hutchinson(1991) [9] and Zheng et al (2007) [10] . Previously it is applied to various elastic problems and heat transfer problems (Ramachandran and Gunjal, 2009 [11] ). Reichel and Chapman(1986) [12] apply this idea to edge wave problems.…”

Section: Introductionmentioning

confidence: 99%

A Boundary Collocation Method for Wave Propagation through Obstacle

Cao¹,

Liu²,

Huang³

et al. 2016

Proceedings of the 2nd International Conference on Electronics, Network and Computer Engineering (ICENCE 2016)

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Abstract. The interaction between wave and the obstacle in water is a common problem in ocean engineering. The article use a new numerical method, Boundary Collocation Method (BCM) based on Eigenfunction Expansion Method (EEM), to solve the two-dimensional wave problems between wave and obstacle. The obstacle is no longer confined to the rectangle, but the submersed wedge obstacle. The change of the wave velocity potential will be analysed.

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Comparison of boundary collocation methods for singular and non-singular axisymmetric heat transfer problems

Cited by 9 publications

References 31 publications

Collocation Trefftz Method for the Heat Conduction Issue in Irregular Domain

Collocation Trefftz Method for the Heat Conduction Issue in Irregular Domain

Weak Stefan Formulation for Bulk Crystal Growth with Non-smooth Interfaces

A Boundary Collocation Method for Wave Propagation through Obstacle

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