Two problems of heat equation in two-component systems.
Keywords:
heat equation, numerical calculation, Dirichlet problem, Robin problem, CAS Maxima.
Abstract
We have investigated a numerical calculation of the temperature field distribution in a one-dimensional system of two components with different thermal characteristic. The calculation involved solving the discretized heat conduction equation utilizing the finite difference method. We use a direct two-step method to solve the corresponding Cauchy problem in the second-order PDE. The case of system cooling from the initial state with a given temperature distribution, and the case of heating the system in the presence of an external heat source are considered.
References
1. Nakhle H. Asmar. Partial Differential Equations with Fourier Series and Boundary Value Problems: Third Edition. − Dover Publications, 2016. − 816 p.
2. S.R.K. Iyengar, R.K. Jain. Numerical Methods. – New Age International Limited Publishers, 2009. – 326 p.
3. W.Y. Yang, W. Cao, T.S. Chung, J. Morris. Applied Numerical Methods using MATLAB. – A John Wiley & Sons, Inc., 2005. – 512 p.
4. Шваліковський Д. М. Моделювання процесів та систем у середовищі CAS Maxima. – Луцьк: ВНУ імені Лесі Українки, 2024. – 252 с.
5. Ryan C. Daileda. Partial Differential Equations: Lecture Handouts & Slides. The 1-D Heat Equation, Part 2. – Trinity University, 2023. – 24 p.
2. S.R.K. Iyengar, R.K. Jain. Numerical Methods. – New Age International Limited Publishers, 2009. – 326 p.
3. W.Y. Yang, W. Cao, T.S. Chung, J. Morris. Applied Numerical Methods using MATLAB. – A John Wiley & Sons, Inc., 2005. – 512 p.
4. Шваліковський Д. М. Моделювання процесів та систем у середовищі CAS Maxima. – Луцьк: ВНУ імені Лесі Українки, 2024. – 252 с.
5. Ryan C. Daileda. Partial Differential Equations: Lecture Handouts & Slides. The 1-D Heat Equation, Part 2. – Trinity University, 2023. – 24 p.
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Published
2024-06-16
How to Cite
Shvalikovskyi , D. (2024). Two problems of heat equation in two-component systems. COMPUTER-INTEGRATED TECHNOLOGIES: EDUCATION, SCIENCE, PRODUCTION, (55), 243-250. https://doi.org/10.36910/6775-2524-0560-2024-55-30
Section
Computer science and computer engineering
