Nonlinear thermal analysis of serrated fins by using homotopy perturbation method

Year 2023, Volume: 29 Issue: 6, 569 - 576, 30.11.2023

İshak Gökhan Aksoy

Abstract

Thermal analysis of serrated fins which are consist of annular and plain sections are investigated. Serrated fin’s thermal conductivity is assumed to change linearly with temperature. Nonlinear differential equations are obtained by applying the energy balance equation for both sections of the serrated fin and these equations are solved by applying homotopy perturbation method. Insulated fin tip, constant fin base temperature and common boundary conditions between the interface of two sections are considered. Serrated fin radii ratio (𝜀), segment height ratio (𝛿),
thermo-geometric fin parameter (𝜓) and thermal conductivity parameter (𝛽) effecting the thermal performance and temperature distribution are investigated. The results showed that the homotopy perturbation is a reliable method for the solutions of such nonlinear differential equations. A very good agreement with the homotopy perturbation method and the numerical finite difference method are obtained. It is seen that, serrated fin efficiency lays between annular and rectangular fins and increases with the increase of segment height ratio and thermal conductivity parameter. Such as, fin efficiency values under the condition of 𝜀 = 2, 𝜓1 = 1.0 and 𝛽 = 0 for 𝛿 = 0, 0.5, and 1 are 0.692, 0.718, and 0.762, respectively.

Keywords

Homotopy perturbation method, Serrated fin, Variable thermal conductivity

Homotopi pertürbasyon yöntemi kullanılarak kesikli dairesel kanatların lineer olmayan ısıl analizi

Abstract

Bu çalışmada, dairesel ve düz kısımlardan oluşan kesikli dairesel kanatçıkların ısıl performansları incelenmiştir. Kanatın ısı iletim katsayısının lineer olarak sıcaklığa bağlı olduğu kabul edilmiştir. Doğrusal olmayan diferansiyel denklemler, kesikli dairesel kanadın her iki bölümü için enerji dengesi denklemi uygulanarak elde edilmiş ve bu denklemler homotopi pertürbasyon yöntemi uygulanarak çözülmüştür. Yalıtılmış kanat ucu, sabit kanat taban sıcaklığı ve iki bölümün ara yüzü arasındaki ortak sınır koşulları göz önünde bulundurulmuştur. Isıl performansı ve sıcaklık dağılımını etkileyen kesik kanat yarıçap oranı (𝜀), kesik kanat yükseklik oranı (𝛿), termo-geometrik kanat parametresi (𝜓) ve ısıl iletkenlik parametresi (𝛽) incelenmiştir. Sonuçlar, homotopi pertürbasyon yönteminin, bu tür doğrusal olmayan diferansiyel denklemlerin çözümleri için güvenilir bir yöntem olduğunu göstermiştir. Homotopi pertürbasyon yönteminin sonuçları ile sayısal sonlu farklar yönteminin sonuçları arasında çok iyi bir uyum elde edilmiştir. Kesikli dairesel kanat veriminin dairesel ve dikdörtgen kanatçıklar arasında yer aldığı ve kesik kanat yükseklik oranının artmasıyla arttığı görülmektedir. Örneğin 𝜀 = 2, 𝜓1 = 1.0 ve 𝛽 = 0 durumunda 𝛿 = 0, 0.5 ve 1 için kanat verimi değerleri sırasıyla 0.692, 0.718 ve 0.762'dir.

Keywords

Homotopi pertürbasyon yöntemi, Kesikli dairesel kanat, Değişken ısıl iletkenlik

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