حل تحلیلی انتقال حرارت در پوسته‌های مخروطی کامپوزیتی ناهمگن با ضرایب هدایت وابسته به دما

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد مهندسی مکانیک دانشگاه صنعتی شاهرود

2 دانشیار دانشکده مهندسی مکانیک دانشگاه صنعتی شاهرود

چکیده

در این مقاله، برای اولین بار یک حل تحلیلی برای انتقال حرارت در پوسته‌های مخروطی کامپوزیتی ناهمگن وابسته به دما ارائه شده است. هندسه پوسته به‌طور کامل مخروطی شکل فرض شده است و الیاف به دور جسم، در جهات دلخواه پیچانده شده‌اند. به­منظور دستیابی به کلی‌ترین حل، شرایط مرزی حرارتی اعمال شده به صورت کلی در پایه پوسته و همچنین اثرات انتقال حرارت هدایتی، جابجایی با جریان سیال اطراف و تشعشع )صورت تقریبی تشعشع( در مرزها مدل شده‌اند. ناهمگن بودن در مسئله حاضر ناشی از وابستگی ضریب انتقال حرارت هدایتی به دما است. بنابراین می‌بایست، معادله انتقال حرارت را ابتدا با استفاده از تبدیل کیرشهف به معادله قابل حل به کمک سری انتگرالی محدود تبدیل کرد، سپس به کمک این تبدیل، معادله دیفرانسیل با مشتقات جزئی به یک معادله دیفرانسیل معمولی مبدل می‌گردد. درنهایت معادله دیفرانسیل حاصل به کمک روش توابع گرین قابل حل است. در آخر با اعمال معکوس تبدیل انتگرالی محدود و معکوس تبدیل کیرشهف توزیع دمای ناهمگن بدست آید. حل حاضر بر اساس مقایسه نتایج حل تحلیلی با حل عددی به روش مرتبه دوم تفاضلات محدود اعتبارسنجی شده است. مفروضات این مسئله به­گونه­ای انتخاب گردیده که  قابلیت حل حاضر برای رفع مشکلات صنعتی درزمینه تولید مخازن تحت فشار مخروطی کامپوزیتی مشخص گردد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Analytical Solution of the Heat Transfer in Heterogeneous Composite Conical Shells with Temperature Dependent Conduction Coefficients

نویسندگان [English]

  • Babak Erfan Manesh 1
  • Mohammad Mohsen Shahmardan 2
  • Mahmood Norouzi 2
1 MSc student, Faculty of mechanical engineering, Shahrood university of technology
2 Associated professor, Faculty of mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
چکیده [English]

This paper presents an analytical solution for heat transfer in heterogeneous composite conical shells with temperature dependent conduction coefficients for the first time. The geometry of the shell is completely conical shaped and the fibers are winded around the laminate in the desired direction. In order to achieve the most general solution, the general boundary condition is considered  at the basis of shell and the effect of heat convection resulted from flow motion around the body and different kinds of non-axisymmetric radiative heat flux at the outer side of the shell is modeled. The heterogeneous effect in this case is the results of the dependency in conduction heat transfer coefficient on temperature. Therefore, the heat transfer equation should first be transformed using the Kirchhoff transform to a solvable equation using integral transformation, then, the partial differential equation becomes an ordinary differential equation Fourier transformation. Finally, the transformed differential equation can be solved Green’s functions. In the end, the reversal integral transformation and reversal Kirchhoff conversion are applied to obtain heterogeneous temperature distribution. Validation of this analytical solution is performed by comparing the analytical results with the solution of second-order finite difference method and some applied cases are considered to investigate the capability of current solution for solving the industrial problems in the production of composite conical pressure vessels.

کلیدواژه‌ها [English]

  • Analytical Solution
  • Composite conical shell
  • Heterogeneous heat transfer
  • Integral transformation
  • Green functions
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