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Mô hình hóa độ dẫn nhiệt và điện bằng cách sử dụng một continuum Cosserat đàn hồi nhớt
Tóm tắt
Chúng tôi xem xét một lý thuyết tuyến tính về một continuum Cosserat đàn hồi nhớt của một loại đặc biệt. Trong quá trình này, chúng tôi liên kết các biến chính đặc trưng cho trạng thái ứng suất-biến dạng của continuum với các đại lượng đặc trưng cho các quá trình điện động lực học và nhiệt. Khi xem xét các tương tự được đề xuất, chúng tôi diễn giải các phương trình mô tả continuum như là các phương trình của nhiệt động lực học và điện động lực học. Chúng tôi xác định các tham số của mô hình bằng cách so sánh các phương trình đạt được với các phương trình Maxwell và phương trình dẫn nhiệt hyperbolic. Kết quả là, chúng tôi có được hai phương trình telegrapher ba chiều: một cho nhiệt độ và một cho vectơ trường điện. Những phương trình này là mới. Chúng mô tả các quá trình điện từ và nhiệt, cũng như cách mà chúng ảnh hưởng lẫn nhau một cách chính xác hơn so với lý thuyết cổ điển. Cụ thể, những phương trình telegrapher này tính đến không chỉ hiệu ứng bề mặt được mô tả trong nhiều nguồn tài liệu về điện động lực học, mà còn cả các hiệu ứng dạng bề mặt tĩnh được quan sát trong một số thí nghiệm. Khác với điện động lực học cổ điển, mà chỉ có hai vectơ vuông góc lẫn nhau: vectơ trường điện và vectơ cảm ứng từ, lý thuyết được đề xuất chứa ba vectơ vuông góc lẫn nhau: vectơ trường điện, vectơ cảm ứng từ và gradient nhiệt độ. Nó đồng nhất với các sự kiện thực nghiệm được phát hiện bởi Ettingshausen và Nernst (hiệu ứng Ettingshausen và hiệu ứng Nernst–Ettingshausen). Nếu bỏ qua thành phần nhiệt, lý thuyết được đề xuất giảm thành hệ phương trình, mà là một tổng quát hóa các phương trình Maxwell. Hệ phương trình này là mới mẻ. Nó là một tương đương ba chiều của các định luật Kirchhoff cho các mạch điện, trong khi các phương trình Maxwell thì không.
Từ khóa
#continuum Cosserat #ứng suất-biến dạng #điện động lực học #nhiệt động lực học #hiệu ứng bề mặt #phương trình telegrapher #điện từ #nhiệt độTài liệu tham khảo
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