{"title":"Approximating the solution of the discharging process in a domestic hot water storage tank","authors":"F. Müller","doi":"10.1080/13873954.2021.1887277","DOIUrl":null,"url":null,"abstract":"ABSTRACT In this article a new approximation procedure for the temperature during the discharging process in a domestic hot water storage tank is developed. The main idea of this procedure is the mathematical description of the dynamic behaviour of a boundary layer that appears inside the storage tank. This leads to an approximate solution of a simple structure but a high accuracy throughout the whole discharging process for the temperature distribution inside the storage tank. For validation the approximate solution is compared with the exact solution that is constructed with help of generalized Fourier coefficients and a numerical solution that is obtained by a semi-discretization method. Adapting the method leads also to an approximation procedure for charging processes.","PeriodicalId":49871,"journal":{"name":"Mathematical and Computer Modelling of Dynamical Systems","volume":"27 1","pages":"141 - 161"},"PeriodicalIF":1.8000,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/13873954.2021.1887277","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical and Computer Modelling of Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/13873954.2021.1887277","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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Abstract
ABSTRACT In this article a new approximation procedure for the temperature during the discharging process in a domestic hot water storage tank is developed. The main idea of this procedure is the mathematical description of the dynamic behaviour of a boundary layer that appears inside the storage tank. This leads to an approximate solution of a simple structure but a high accuracy throughout the whole discharging process for the temperature distribution inside the storage tank. For validation the approximate solution is compared with the exact solution that is constructed with help of generalized Fourier coefficients and a numerical solution that is obtained by a semi-discretization method. Adapting the method leads also to an approximation procedure for charging processes.
期刊介绍：
Mathematical and Computer Modelling of Dynamical Systems (MCMDS) publishes high quality international research that presents new ideas and approaches in the derivation, simplification, and validation of models and sub-models of relevance to complex (real-world) dynamical systems.
The journal brings together engineers and scientists working in different areas of application and/or theory where researchers can learn about recent developments across engineering, environmental systems, and biotechnology amongst other fields. As MCMDS covers a wide range of application areas, papers aim to be accessible to readers who are not necessarily experts in the specific area of application.
MCMDS welcomes original articles on a range of topics including:
-methods of modelling and simulation-
automation of modelling-
qualitative and modular modelling-
data-based and learning-based modelling-
uncertainties and the effects of modelling errors on system performance-
application of modelling to complex real-world systems.
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