نوع مقاله: مقاله پژوهشی

نویسندگان

1 استادیار، مهندسی مکانیک، دانشگاه یاسوج، یاسوج ، ایران

2 دانشجوی کارشناسی ارشد، مهندسی مکانیک، دانشگاه یاسوج، یاسوج، ایران

چکیده

در این مقاله یک راه حل تحلیلی دقیق برای هدایت گرمایی درون یک ماده مدرج تابعی که خواص مواد آن دارای تابعیت نمایی نسبت به مکان و تابعیت خطی نسبت به دما داشته باشد، ارائه شده است. به‌دلیل وابستگی خواص مواد به دما، معادله حاکم غیر خطی شده و نمی‌توان آن را به‌طور مستقیم حل کرد. اساس روش حل تحلیلی پیشنهاد شده استفاده از یک تبدیل انتگرالی می‌باشد، که این تبدیل معادله میدان دمای غیر‌خطی را به یک معادله خطی تبدیل می‌کند. همچنین لازم است شرایط مرزی مناسب توسط تبدیل به‌کار رفته، استفاده شود. سپس معادله خطی شده حل و سپس میدان دمای تبدیل یافته به‌دست می‌آید. پس از آن از یک تبدیل معکوس استفاده می‌شود تا میدان دمای فیزیکی به‌دست آید. در نهایت از این روش دو مسئله هدایت درون یک استوانه یک بعدی در جهت شعاع و مسئله هدایت درون پوسته کروی حل می‌شود. برای اعتبارسنجی و اطمینان از حل ریاضی انجام شده، نتایج با حل عددی مسئله مقایسه و تطابق کاملی مشاهده شد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Exact solution of steady nonlinear heat conduction in exponentially graded cylindrical and spherical shells with temperature-dependent properties

نویسندگان [English]

  • Amin Moosaie 1
  • Hamed Panahi Kalus 2

1 Department of Mechanical Engineering, Yasouj University, Yasouj, Iran

2 Department of Mechanical Engineering, Yasouj University, Yasouj, Iran

چکیده [English]

In this study, an exact analytical solution of steady heat conduction problem in exponentially graded inhomogeneous materials with temperature-dependent heat conductivity is presented. The FGM properties are assumed to depend exponentially on spatial coordinates whereas the temperature dependency is taken to be a linear function. The proposed method is based on an integral transformation of the temperature field, which transforms the nonlinear heat equation into a linear one for the transformed temperature. The boundary conditions are to be transformed as well. Once the linear equation is solved and the transformed temperature is obtained, the inverse transform is used to calculate the physical temperature field. The boundary conditions are enforced on the transformed temperature. Finally, in order to demonstrate the application of the proposed method, two numerical examples are worked out, i.e. nonlinear heat conduction in the radial direction of cylindrical and spherical thick-walled shells. In order to check the validity of the proposed solution scheme, a numerical solution of the problems has been performed and an excellent agreement has been established

کلیدواژه‌ها [English]

  • Nonlinear heat conduction
  • temperature-dependent heat conductivity
  • exponentially graded material
  • Hollow Cylinder
  • hollow sphere

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