حل تحلیلی انتقال حرارت در یک مخروط ساخته شده از مواد مدرج تابعی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه صنعتی شاهرود

2 دانشگاه بجنورد

3 بجنورد-فنی و مهندسی- گروه مهندسی مکانیک

چکیده

در این مطالعه، مساله انتقال حرارت هدایتی دوبعدی در یک مخروط توخالی ناقص ساخته شده از مواد مدرج تابعی مورد بررسی قرار گرفته و یک حل تحلیلی دقیق ارائه شده است. در مطالعه حاضر، خواص مواد مطابق با یک تابع توانی تغییر می‌کند. شرایط مرزی حرارتی نیز به‌صورت غیرهمگن فرض شده است. از روش جدایی متغیرها برای تعیین دقیق توزیع دمای پایا در مخروط استفاده شده است. حل بدست آمده با استفاده از داده‌های عددی صحت‌سنجی شده است. برای اثبات توانایی حل حاضر، یک مثال کاربردی که در معرض شرایط مرزی ترکیبی قرار دارد، مورد مطالعه قرار گرفته است. اثرات پارامترهای موثر در توزیع دما برای هندسه حاضر مورد بررسی قرار گرفته است. نتیجه این مطالعه برای روشن شدن روند طراحی و بهینه‌سازی هندسه‌های نسبتا پیچیده از مواد مدرج تابعی مفید خواهد بود. همچنین با توجه به تحلیلی بودن حل حاضر، نتایج حاصل از این مطالعه می‌تواند برای فهم بهتر مکانیزم‌های انتقال حرارت مواد مدرج تابعی مفید باشد.در مساله حاضر با افزایش مقدار  و ، هدایتپذیری حرارتی به ترتیب به میزان حدود 8 و 2 درصد افزایش یافته که منجر به افزایش توزیع دمای مخروط خواهد شد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Analytical Solution of Heat Transfer in a Cone Made of Functionally Graded Material

نویسندگان [English]

  • Amin Emamian 1
  • Amin Amiri Delouei 2
  • Sajjad Karimnejad 1
  • Hasan Sajadi 3
1 Shahrood University of Technology
3 بجنورد-فنی و مهندسی- گروه مهندسی مکانیک
چکیده [English]

In the current study, the problem of two-dimensional steady-state heat conduction in a truncated hollow cone made of functionally graded materials is referred and an exact analytical solution is presented. In the present study, the properties of a material are modified in accordance with a power function. The thermal boundary conditions are also assumed to be non-homogeneous. The separation of variable method is implemented to acquire the exact steady-state temperature distribution. The obtained solution is adequately verified using numerical data. To further demonstrate the ability of the solution, an illustrative case that is exposed to a combination of boundary conditions is studied. In particular, the influences of effective parameters on the temperature distribution are investigated for the current geometry. The outcome of this study would be helpful to shed light on the process of designing and optimizing relatively complex geometries. Also, considering the analyticity of the present solution, the results of this study can be useful for a better understanding of the heat transfer mechanisms of functionally graded materials. In the present case, increasing the amount of m and κ, the thermal conductivity increased by about 8 and 2 percent respectively, which would increase the distribution of cone temperature.

کلیدواژه‌ها [English]

  • Functionally graded materials
  • heat transfer
  • Exact Solution
  • Cone
  • Separation of variable method
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