Isıl parametreleri değişken olan dairesel kanatların parametrelerin değişimi yöntemi kullanılarak optimizasyonu

Bu çalışmanın amacı, ısıl özelliklerin sıcaklıkla değiştiği dairesel kanatların optimum tasarımı için, tasarımcıya kullanışlı korelasyon denklemleri sunmaktır. Kanatların optimum boyutlarını elde etmek için kanattan olan ısı transferinin mümkün olan en az kabulle hesaplanması gerekir. Bu nedenle, bu çalışmada ısı taşınım katsayısı ve ısıl iletkenliğin sıcaklıkla değişimi göz önüne alınmış ve lineer olmayan kanat denklemi, nonlinear problemlerin çözümünde kullanımı çok yeni olan parametrelerin değişimi yöntemi ile çözülmüş, elde edilen sıcaklık dağılımı yardımıyla kanattan çevreye olan ısı transfer hızı boyutsuz problem parametreleri cinsinden hesaplanmıştır. Verilen problem parametreleri için ısı transfer hızını maksimum yapan kanat geometrileri saptanmıştır. Kaynama, doğal taşınım ve zorlanmış taşınımla ısı transfer modları için kullanılabilecek bu sonuçlar iki eş korelasyon denklemi ile tasarımcının hizmetine sunulmuştur.

Anahtar Kelimeler:

Dairesel kanatlar, Optimizasyon, Doğrusal olmayan diferansiyel denklemler, Değişken ısıl iletkenlik, Değişken ısı taşınım katsayısı

Variation of parameters method for optimizing annular fins with variable thermal properties

The aim of this study is to offer useful correlation equations to the designer for the optimum design of annular fins with thermal properties varying with temperature. In order to obtain the optimum size of the fins, the heat transfer from the fin must be calculated with the least assumptions possible. Therefore, the variation of the heat transfer coefficient and thermal conductivity with the temperature are considered in this study and a nonlinear fin equation is solved with the variation of parameters method, which is quite new in the solution of nonlinear heat transfer problems. Heat transfer rate from the fin to the environment is calculated in terms of dimensionless problem parameters with the help of the obtained temperature distribution. Fin geometries maximizing the heat transfer rate are determined for the given problem parameters. These results, which can be used for nucleate boiling, natural convection and forced convection heat transfer modes, are offered to the designer with two identical correlation equations.

Keywords:

Annular fins Optimization, Variable thermal conductivity, Nonlinear differential equations, Variable heat transfer coefficient, Variation of parameters method,

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