• 제목/요약/키워드: Stefan problem

검색결과 35건 처리시간 0.022초

Level Set 방법에 의한 상경계 추적 수치기법 연구 (Study on the Phase Interface Tracking Numerical Schemes by Level Set Method)

  • 김원갑;정재동
    • 대한설비공학회:학술대회논문집
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    • 대한설비공학회 2006년도 하계학술발표대회 논문집
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    • pp.116-121
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    • 2006
  • Numerical simulations for dendritic growth of crystals are conducted in this study by the level set method. The effect of order of difference is tested for reinitialization error in simple problems and authors founded in case of 1st order of difference that very fine grids have to be used to minimize the error and higher order of difference is desirable to minimize the reinitialization error The 2nd and 4th order Runge-Kutta scheme in time and 3rd and 5th order of WENO schemes with Godunov scheme are applied for space discretization. Numerical results are compared with the analytical theory, phase-field method and other researcher's level set method.

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Micro Bonding Using Hot Melt Adhesives

  • Bohm, Stefan;Hemken, Gregor;Stammen, Elisabeth;Dilger, Klaus
    • 접착 및 계면
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    • 제7권4호
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    • pp.28-31
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    • 2006
  • Due to the miniaturization of MEMS and microelectronics the joining techniques also have to be adjusted. The dosing technology with viscous adhesives does not permit reproducible adhesive volumes, which are clearly under a nano-liter. A nano-liter means however a diameter of bonding area within the range of several 100 micrometers. Additional, viscous adhesives need a certain time, until they are cross linked or cured. The problem especially in the MEMS is the initial strength, since it gives the time, which is needed for joining an individual adhesive joint. The time up to the initial strength is with viscous, also with fast curing systems, within the range of seconds until minutes. Until the reach of the initial strength, the micro part must be fixed/held. Without sufficient adjustment/clamping it can come to a shift of the micro parts. Also existing micro adhesive bonding processes are not batch able, i.e. the individual adhesive joints of a micro system must be processed successively. In the context of the WCARP III 2006 now an innovative method is to be presented, how it is possible to solve the existing problems with micro bonding. i.e. a method is presented, which is batch able, possess a minimum joining geometry with some micrometers and is so fast that no problems with the initial strength arise. It is a method, which could revolutionize the sticking technology in the micro system engineering.

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상변화 물질의 용융과정에 있어서 좌표변환을 이용한 온도분포의 해석적 연구 (The finite difference analysis on temperature distribution by coordinate transformation during melting process of phase-change Material)

  • 김준근;임장순
    • 태양에너지
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    • 제5권2호
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    • pp.77-83
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    • 1985
  • An analysis is performed to investigate the influence of the buoyancy force and the thickness variation of melting layer in the containment that is filled with phase-change Material surrounding a cylindrical heating tube during melting process. The phase-change material is assumed to be initially solid at its phase-change temperature and the remaining solid at any given time is still at the phase-change temperature and neglecting the effect of heat transfer occuring within the solid. At the start of melting process, the thickness of melting layer is assumed to be a stefan-problem and after the starting process, the change of temperature and velocity is calculated using a two dimensional finite difference method. The governing equations for velocity and temperature are solved by a finite difference method which used SIMPLE (Semi Implicit Method Pressure linked Equations) algorithm. Results are presented for a wide range of Granshof number and in accordance with the time increment and it is founded that two dimensional fluid flow occurred by natural convection decreases the velocity of melting process at the bottom of container. The larger the radius of heating tube, the higher heat transfer is occurred in the melting layer.

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상변화물질의 대류유동 및 열전달 현상에 관한 연구 (Study of Convective Flow and Heat Transfer Phenomena in the Phase Change Material)

  • 손상석;이채문;이재헌;임장순
    • 태양에너지
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    • 제6권2호
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    • pp.43-53
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    • 1986
  • The objective of this study is to report on the characterics of convective flow and heat transfer during metling process in order to provide design information for thermal energy storage systems which use phase change material. In present study, flow and heat transfer characteristics of the Phase Change Material in the Open Top Model (O.T.M) and in the Closed Top Model (C.T.M) were studied numerically by the control volume formulation using the algebraic non-orthogonal coordinate transformation. For the calculation procedure, the physical properties of fluid are assumed to be constant except density which is linely dependent on temperature in the bouyancy term of momentum equations. At start of melting process, the thickness of melting layer is assumed from the Stefan Problem assumption. The heat transfer results of Open Top Model and Closed Top Model are compared with the parameters of Grashof number and aspect ratio. It was found that heat transfer phenomena in melted region was greatly affected by buoyancy-driven natural convection and the melting distance of Open Top Model at the upper region is greater than that of Closed Top Model.

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Weakly Complementary Cycles in 3-Connected Multipartite Tournaments

  • Volkmann, Lutz;Winzen, Stefan
    • Kyungpook Mathematical Journal
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    • 제48권2호
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    • pp.287-302
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    • 2008
  • The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles $C_1$ and $C_2$ such that V(D) = $V(C_1)\;{\cup}\;V(C_2)$, and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles $C_1$ and $C_2$ such that $V(C_1)\;{\cup}\;V(C_2)$ contains vertices of all partite sets of D. The problem of complementary cycles in 2-connected tournaments was completely solved by Reid [4] in 1985 and Z. Song [5] in 1993. They proved that every 2-connected tournament T on at least 8 vertices has complementary cycles of length t and ${\mid}V(T)\mid$ - t for all $3\;{\leq}\;t\;{\leq}\;{\mid}V(T)\mid/2$. Recently, Volkmann [8] proved that each regular multipartite tournament D of order ${\mid}V(D)\mid\;\geq\;8$ is cycle complementary. In this article, we analyze multipartite tournaments that are weakly cycle complementary. Especially, we will characterize all 3-connected c-partite tournaments with $c\;\geq\;3$ that are weakly cycle complementary.