Analysis of thermal performance of annular fins with variable thermal conductivity by homotopy analysis method

Bu çalışmada, ısıl iletkenliği sıcaklıkla değişen dairesel kanatların ısıl performansını incelemek için homotopi analiz yöntemi kullanılmıştır. Yöntemin algoritması, çözümün doğruluğu ve yakınsaklığını kontrol eden bir parametre içerdiğinden, sonuçlar hatanın çözüm anında hesaplanmasıyla doğrulanabilir. HAM, pertürbasyon yöntemlerinin aksine çok geniş problem parametreleri aralıkları için yakınsak çözümler vermektedir. Bu çalışmada dairesel kanatların verimleri üç problem parametresi cinsinden elde edilmiştir. Çözümden elde edilen veri yardımıyla kanat verimi için korelasyon denklemleri üretilmiştir. Korelasyon denklemleri ısı iletim katsayıları sıcaklıkla değişen dairesel kanatların tasarımı için kullanılabilir.

Isıl iletkenliği sıcaklıkla değişen dairesel kanatların performansının homotopi analiz yöntemi ile incelenmesi

The homotopy analysis method (HAM) is used to analyze the thermal performance of annular fins with temperature-dependent thermal conductivity. Since the HAM algorithm contains a parameter that controls the convergence and accuracy of the solution, its results can be verified internally by calculating the residual error. The HAM solution appears in terms of algebraic expressions which are not only easy to compute but also give highly accurate results covering a wide range of values of the parameters rather than the small values dictated by the perturbation solution. In this work, the fin efficiency of nonlinear annular fins is obtained as a function of thermogeometric fin parameter, thermal conductivity parameter and radii ratio. The data from the present solutions is correlated for suitable ranges of problem parameters. The resulting correlation equations can assist thermal design engineers for designing of annular fins with temperature-dependent thermal conductivity.

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