Thermal management of parabolic pin fin subjected to a uniform oncoming airflow: optimum fin dimensions
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Thermal management of parabolic pin fin subjected to a uniform oncoming airflow: optimum fin dimensions Mustafa Turkyilmazoglu1,2 Received: 5 January 2020 / Accepted: 21 October 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract A concave-parabolic pin fin (spine) is considered within the present research. The thermal property of the spine is exhibited to be affected by a uniform oncoming airflow in an aim at improving its cooling performance. The mathematical model corresponding to one-dimensional physical layout is formulated first from the usual heat balance method. Exact and numerical solutions of the fin temperature distribution are then extracted from the model, relying upon two physical parameters: namely, the Peclet number Pe, controlling the magnitude of the airflow and the fin shape parameter 𝛼 , adjusting the spine shape. It is shown that these parameters have high impacts on the performance of the parabolic pin fin towards cooling the medium it is attached to. Finally, optimum concave parabolic pin fins corresponding to a given volumetric region are identified by means of maximizing the base heat transfer rate. Interestingly, the optimum dimensions of the spine are found to be much influenced by the variation in Peclet number. Keywords Parabolic pin fin · Uniform airflow · Analytical solution · Temperature resolution · Base heat transfer rate · Optimum dimensions
Introduction The interest in the analysis of various pin fin profiles [1] is growing recently in order to search for performance of such fins in different operational mediums and to optimize the fin shape within the operational conditions. Pin fin heat transfer devices are frequently used in industrial applications for the purpose of cooling process by increasing the rate of heat transfer, see for instance [2–4] and [5]. The present work is dedicated to the theoretical thermal performance analysis of the pin fin of a concave parabolic shape, when it is exposed to a uniform oncoming airflow. The extended surface literature is now replete with the study of traditional fins and of their thermal efficiency analysis; one can refer to the articles [6–8] and [9, 10], amongst many others. Pin fins under static conditions received great attention commencing from the pioneering work of Bejan * Mustafa Turkyilmazoglu [email protected] 1
Department of Mathematics, Hacettepe University, Beytepe, 06532 Ankara, Turkey
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
2
and Morega [11] on the optimal plate-fin arrays with cylindrical pin fins. Pakrouh et al. [12] obtained the configurations maximizing the pin fin heat sink operational time using paraffin. It was theoretically found in [13, 14] that the right treatment of arc length modifies the optimal pin fin profile from the parabolic pin fin to stepped pin fin. The experimental data by Aliabadi et al. [15] disclosed that the thermal and hydrodynamic characteristics of pin-fin miniature heat sink are much affected when sub
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