İki Boyutlu Anizotropik Plakanın Isı İletim Analizi

Öz

Homojen olmayan genel sınır koşullarına sahip iki boyutlu anizotropik bir plakanın ısı iletim problemi, kartezyen koordinat sisteminde ANSYS Fluent kullanılarak çözülmüştür. Malzemenin termal iletkenliği ve ısı üretiminin keyfi olarak iki uzay değişkeni yönünde değiştiği varsayılmıştır. Bu koşullar altında sistemi modelleyen değişken katsayılı diferansiyel denklem elde edilir. Bu tür denklemlerin analitik çözümleri, bazı basit malzeme fonksiyonları dışında elde edilemez. İki uzay değişkenine bağlı olarak değişen ısı iletim katsayısı ve hacimsel ısı üretimi ile homojen olmayan sınır koşullarını içeren değişken katsayılı diferansiyel denklem ANSYS Fluent kullanıcı tanımlı fonksiyon (UDF) ile sayısal olarak ele alınmıştır. Sayısal yöntemin doğruluğu, basit malzeme fonksiyonları kullanılarak analitik ve sayısal çözümler karşılaştırılarak gösterilmiştir.

Anahtar Kelimeler

• Anizotropik Isı iletimi
• Analitik çözüm
• Sonlu elemanlar yöntemi
• UDF

Heat Conduction Analysis of Two-Dimensional Anisotropic Plate

Öz

The heat conduction of a two dimensional anisotropic plate with non-homogeneous general boundary conditions is solved by using ANSYS Fluent in the cartesian coordinate system. It is assumed that the thermal conductivity and heat generation of the material arbitrarily change in the direction of the two space variables. Under these conditions, a variable coefficient differential equation is obtained. Analytical solutions of such equations cannot be obtained except for some simple material functions. The variable coefficient differential equation, which includes the heat conduction coefficient and volumetric heat generation depending on the two space variables and non-homogeneous boundary conditions, is handled numerically by ANSYS Fluent user-defined function (UDF). The accuracy of the numerical method is demonstrated by comparing analytical and numerical solutions using simple material functions.

Anahtar Kelimeler

• Anisotropic heat conduction
• Analytical solution
• Finite element method
• UDF

Kaynakça

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