باله متخلخل همرفت طبیعی با هدایت حرارتی و گرمای داخلی وابسته به دما با استفاده از چند جمله‌ای‌های چبیشف بهینه شده با الگوریتم نقطه درونی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشیار گروه ریاضی کاربردی، دانشکده علوم پایه، دانشگاه بین المللی امام خمینی، قزوین، ایران

2 استادیار گروه ریاضی، مرکز آموزش عالی فنی مهندسی بوئین زهرا، بوئین زهرا، قزوین، ایران

3 استادیار گروه ریاضی، واحد مریوان، دانشگاه آزاد اسلامی، مریوان، ایران

چکیده

در این مقاله، تجزیه و تحلیل رفتار حرارتی باله متخلخل همرفت طبیعی با تولید گرمای داخلی هدایت حرارتی وابسته به درجه حرارت مورد بررسی قرار می‌گیرد. مدل‌های انتقال گرمای نمادین توسعه‌یافته، به منظور بررسی اثرات پارامترهای مختلف عملکرد حرارتی باله متخلخل در نظر گرفته شده است. با توجه به فرمول‌بندی مساله، یک رویکرد محاسباتی هوشمندانه جدید برای جستجوی جواب،‌ ایجاد شده است. برای رسیدن به این هدف، معادله دیفرانسیل غیرخطی مساله، به یک مساله معادل تبدیل شده است که شرایط مرزی آن به‌گونه‌ایاست که به‌راحتی می‌توان از چندجمله‌ای چبیشف اصلاح شده نوع اول استفاده نمود. توابع مبتنی بر چندجمله‌ای چبیشف، سری جواب تقریبی با وزن‌های مجهول را ایجاد می‌نماید. فرمول ریاضی مساله بهینه‌سازی شامل یک خطای قابل کنترل است که با تنظیم وزن‌ها با استفاده از روش نقطه درونی به حداقل می‌رسد. جواب تقریبی آزمایشی با تحمیل تلورانس محدود شده در مساله بهینه‌سازی اعتبارسنجی شده است. به‌علاوه نتایج به‌دست آمده دقیق‌تر از نتایج گزارش شده در تحقیقات قبلی است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Natural convection porous fin with temperature-dependent thermal conductivity and internal heat generation via optimized Chebyshev polynomials with interior point algorithm

نویسندگان [English]

  • Elyas Shivanian 1
  • Mahdi Keshtkar 2
  • Hedayat Fatahi 3
1 Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34148-96818, Iran
2 Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran
3 Department of Mathematics, Marivan Branch, Islamic Azad University, Marivan, Iran.
چکیده [English]

In this study, thermal behaviour analysis of a natural convection porous fin with internal heat generation and temperature dependent thermal conductivity is revisited. The developed symbolic heat transfer models are for the purpose of the investigation of the effects of different parameters on the thermal performance of the porous fin. Regarding the problem formulation, a novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing nonlinear differential equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Furthermore, the obtained results are more accurate than those reported in previous researches.

کلیدواژه‌ها [English]

  • Chebyshev polynomial of the first kind
  • Interior point method
  • Natural convection
  • Porous fin
  • Thermal performance
  • Temperature-dependent thermal conductivity
  • Internal heat generation
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