Exact Closed-Form Result for the Heat Transfer From Convecting-Radiating Fin of Rectangular Shape
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
E. Shivanian
1
(
Department of Applied Mathematics, Imam Khomeini International
University, Qazvin, Iran.
)
F. Sohrabi
2
(
Department of Applied Mathematics, Imam Khomeini International University, Qazvin, Iran.
)
کلید واژه: Fin efficiency, Heat transfer rate, Exact analytical solution, Temperature distribution, Unique solution,
چکیده مقاله :
In this letter, the problem of determining heat transfer from convecting-radiating fin of rectangular shape is investigated. We consider steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. It is demonstrated that the governing fin equation is exactly solvable. The exact, closed-form analytical solutions in implicit form are convenient for physical interpretation and optimization for maximum heat transfer.
در این مقاله، مساله تعیین انتقال حرارت از فین تابشی به شکل مستطیل بررسی می شود. ما حرارت یک بعدی و پایا در پره در نظر می گیریم و از تبادل تابشی بین پره های مجاور و بین پره و سطح اولیه آن صرفنظر می کنیم. نشان داده می شود که معادله فین حاکم، که یک معادله دیفرانسیل درجه دوم غیر خطی است، بصورت دقیق قابل حل است. جوابهای تحلیلی دقیق و به فرم بسته به شکل ضمنی برای تفسیر فیزیکی و بهینه سازی برای حداکثر انتقال حرارت مناسب ارایه می شود. علاوه بر این، جواب تحلیلی دقیق برای سرعت انتقال حرارت و بازده فین می شود.
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