DOĞRUSAL OLMAYAN SINIR KOŞULLARINA SAHİP ISI TRANSFERİ PROBLEMLERİNİN SINIR ELEMAN YÖNTEMİ İLE ANALİZİNE YÖNELİK YENİ BİR FORMÜLASYON

Abstract

Bu çalışmada Fourier denklemi ile ifade edilen ısı transferi problemlerinin bir ya da daha fazla bölgesinde tanımlı doğrusal olmayan sınır koşulları altında çözümüne yönelik sınır eleman yöntemi tabanlı etkili bir sayısal çözüm sunulmaktadır. Çözüm, sınır eleman yöntemi sistem matrislerinin üzerinde yapılan matematiksel işlemler ile bilinmeyenleri sadece doğrusal olmayan sınır bölgesindeki sıcaklık farkı olan indirgenmiş matris denklemleri elde etmektedir. Bu sayede doğrusal olmayan sınır koşullarına dayalı iterasyonlar daha hızlı gerçekleştirilebilmektedir. Doğrusal olmayan sınır koşullarının tanımlı olduğu bölgelerde çözüm elde edildikten sonra tüm sınır çözümü tanımlı bir son-işlem ile gerçekleştirilebilmektedir. Gerçek çözümü elde edilmiş bir örnek kullanılarak elde edilen sonuçlar değerlendirilmiştir.

Keywords

• Sınır eleman yöntemi
• ısı transferi
• lineer (doğrusal) olmayan sınır koşulları

A NEW FORMULATION FOR THE BOUNDARY ELEMENT ANALYSIS OF HEAT CONDUCTION PROBLEMS WITH NONLINEAR BOUNDARY CONDITIONS

Abstract

An effective numerical method based on the boundary element formulation is presented to solve heat conduction equations which are governed by the Fourier equation, with nonlinear boundary conditions on one or more sections of the prescribed boundary. The solution involves the manipulation of the system matrices of the boundary element method and obtaining a smaller ranked matrix equation in which the unknown is only the temperature difference over the nonlinear boundary condition region. This way, the iterations to deal with the nonlinear conditions are performed faster. After finding the solution over the nonlinear boundary condition region, the solution over the entire boundary is obtained as a post-process through a prescribed relation. An example with a proven exact solution is employed to assess the results.

Keywords

• Boundary element method
• heat conduction
• nonlinear boundary conditions

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