A Study on Heat Equation
數學熱傳導方程的研究 – 數學系廖倪徵

Liao Nizheng is one of the 2020/2021 outstanding graduates in the Department of Mathematics. His final year project is about heat conduction equation which covers its physical background, the derivation of mathematical model, the design and analysis of numerical method, as well as numerical experiments by coding the algorithm with C++ language. ‘Using the mathematical heat equation model, it can calculate the speed of iron heat transfer and air propagation (such as air-conditioning or heating). It can also calculate the duration of making a certain space cooler or warmer.’ Liao NiZheng explains. Through this research, the physical mechanism behind the heat equation is well understood, classical theoretical results related to heat equation, e.g., the stability and convergence are confirmed by the numerical results. The code developed in this work would be used for further study.

Liao NiZheng was first attracted by UM’s environment, and later he discovered the UM academic staff are knowledgeable and very professional. Liao NiZheng said that he has benefited a lot from cooperating with professors in his graduation project, and he also learned to complete an academic thesis independently. During the preparation process, ‘I have learned a lot about programming skills and physics knowledge that could be very useful in the future, and at the same time I have clarified many practical problems. These abilities are all improved through hands-on practices in this project.’ Liao NiZheng says. Four-year higher education in UM has also changed Liao NiZheng’s values and ways of doing things, he used to focus on the outcomes and only seek good grade in the exam. Now he pays more attention to the process and  willing to explore more and find out the reasons behind, he is having a new understanding of not only Mathematics but also his own life. In the near future, he is going to study a master degree in UM and will continue his journey of exploration in Mathematics.

廖倪徵是2020/2021學年數學系優秀本科畢業生，經過學院的遴選，他的畢業設計作品獲選成為「最佳優秀作品項目」之一，他的作品是對數學熱傳導方程進行研究，研究內容包括其物理背景、數學模型的推導、數值方法的設計與分析，以及用C++語言編寫算法的數值實驗。廖倪徵解釋說:「利用氣體及固體的數學熱方程模形，可以計算到鐵傳熱及空氣傳播(如冷氣或暖氣) 的速度，例如需要多少分鐘才可以令一塊鐵提升至某溫度或多久可以令一間房間變冷或暖。」畢業設計作品為熱傳導方程背後的物理機制提供更好的理解。另一方面，與熱傳導方程相關的經典理論結果，例如穩定性和收斂性，也得到了數值結果的重新推導和證實, 而作品中開發的代碼將用於未來研究。

由最初被澳大的環境吸引，到後來發現澳大師資十分優越，廖倪徵表示在畢業設計作品與老師們共同合作，令他獲益良多，也學會了獨立完成一篇學術論文。在準備的過程中，廖倪徵說: 「我學會很多對未來有用的編程技巧、物理知識等，同時也釐清很多現實問題，這些技巧皆是透過畢業設計作品親身實踐來提升。」四年教育不光在學術研究上，在獨立思考、為人處世態度乃至價值觀方面都令廖倪徵獲益匪淺。由最初只重視結果、專注表面、只求考試表現優良，現在的他更重視過程，樂於探索及深思當中的原由，對數學及對自己的未來也有了新認知。未來，他將在澳大升讀碩士，繼續數學的學習之旅。