افتح

توقع التوزيع الحراري في زعنفة متموجة متحركة باستخدام طريقة جديدة لتدريب الشبكات العصبية المستنيرة بالفيزياء

قائمة الرموز

الرمز الفرعي

• معدلات نقل الحرارة المتدفقة والتقلبات الحرارية الديناميكية في الزعنفة المتموجة.
• تأثير توليد الحرارة الداخلية على التغير الحراري للزعانف المتموجة.
• حل نموذج نقل الحرارة المطور مع تطبيق PINN.
• دقة PINN المطبقة في حل معادلات نقل الحرارة غير الخطية.

صياغة المشكلة

• يفترض أن الزعنفة تنقل الحرارة مع البيئة المحيطة التي لها درجة حرارة ثابتة من خلال الحمل الحراري.
• يحدث نقل الحرارة من السطح الممتد إلى السائل المجاور في حالة مستقرة.
• يفترض أن الموصلية الحرارية وتوليد الحرارة الداخلية ومعامل نقل الحرارة بالحمل تعتمد على درجة الحرارة.
• يعتبر المحور السيني على طول الطول الكلي للزعانف، في البداية عند سطحها الأساسي.
• مقاومة الحرارة عند نقطة التفاعل بين الزعنفة والجدار غير مهمة.
• يتم اعتبار درجة حرارة السائل المجاور ودرجة حرارة قاعدة الزعنفة ثوابت.
• نظرًا لأن سمك الزعنفة صغير بالنسبة للقياسات المتبقية، يمكن تقريب توزيع درجة الحرارة في الزعنفة كدالة تعتمد فقط على إحداثيات الطول.

الشكل 1. التصوير الهندسي لزعانف متموجة.

الشبكات العصبية المدعومة بالفيزياء (PINNs)

الشكل 2. إجراء العمل لنموذج الشبكة العصبية المعتمد على الفيزياء.

النتائج والمناقشة

الشكل 3. مقارنة نتائج PINN و RKF-45.

الشكل 4. تأثير على من WFRS.

الشكل 5. تأثير على من WFRS.

الشكل 6. تأثير على من WFRS.

الشكل 7. تأثير على من WFRS.

الشكل 8. نتائج MSE لتدريب PINN لعدد مختلف من الخلايا العصبية.

الشكل 9. خسارة التدريب لتدريب الشبكة العصبية الفيزيائية (PINN).

الشكل 10. رسم بياني للخطأ لنتائج MAE لتدريب PINN.

الخاتمة

• زيادة في متغير الموصلية الحرارية تؤدي إلى زيادة في تباين درجة الحرارة في الزعنفة المتموجة.
• يلاحظ انخفاض في التغير الحراري مع زيادة في معامل الحمل الحراري والتوصيل.
• تؤدي المستويات المرتفعة من معلمة توليد الحرارة الداخلية إلى تعزيز التشتت الحراري في الزعنفة ذات الشكل الموجي.
• الملف الحراري للزعنفة المتموجة يتزايد مع ارتفاع مؤشر معلمة عملية الحمل الحراري.
• وفقًا للنتائج، أظهر الشبكة العصبية المعتمدة على الفيزياء (PINN) توافقًا ملحوظًا مع النتائج العددية خلال التدريب. وقد تفوقت الشبكة، المعززة بالخصائص المصممة، في التقاط الفيزياء الأساسية للمشكلة. ونتيجة لذلك، تفوقت على الشبكات العصبية التقليدية في قدرتها على تقديم توقعات دقيقة خارج بيئة التدريب.
• تجمع خصائص النمذجة التقليدية المعتمدة على الفيزياء مع القدرة على التكيف والتعلم لشبكة الأعصاب المعتمدة على الفيزياء. إنها توفر حلاً دقيقًا وفعالًا، مما يقلل من الحاجة إلى مجموعات بيانات ضخمة ويقلل من التكاليف الحاسوبية مع الحفاظ على دقة عالية من خلال تضمين المعادلات الحاكمة بشكل صريح في بنية الشبكة العصبية.

توفر البيانات

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شكر وتقدير

مساهمات المؤلفين

المصالح المتنافسة

معلومات إضافية

OPEN

Predicting the thermal distribution in a convective wavy fin using a novel training physics-informed neural network method

List of symbols

Subscript

• Convective heat transfer rates and dynamic thermal fluctuations in a wavy fin.
• Influence of internal heat generation on the thermal variation of the wavy fin.
• Solution of the developed heat transfer model with the application of PINN.
• Precision of the applied PINN in solving the heat transfer nonlinear equations.

Formulation of the problem

• The fin is presumed to transmit heat with the surrounding environment having conatant temperature through convection.
• Transfer of heat from the extended surface to the adjacent fluid occurs in a steady state.
• The thermal conductivity, internal heat generation and convective heat transfer coefficient are supposed to be temperature-dependent.
• The x -axis is regarded along the overall length of the fin, initially at its primary surface.
• The heat resistance at the point of interacting between the fin and the wall is insignificant.
• The temperature of the adjacent fluid , and the fin-base temperature are taken to be constants.
• Since the fin thickness is small in regard to the remaining measurements, the temperature distribution throughout the fin can be approximated as a function of only the length coordinate.

Figure 1. Geometrical depiction of a wavy fin.

Physics-informed neural networks (PINNs)

Figure 2. Working procedure of PINN.

Results and discussion

Figure 3. Comparison of PINN and RKF-45 results.

Figure 4. Influence of on of WFRS.

Figure 5. Influence of on of WFRS.

Figure 6. Influence of on of WFRS.

Figure 7. Influence of on of WFRS.

Figure 8. MSE results of the PINN training for different neurons.

Figure 9. Training loss of the PINN training.