Teaching differential equations through modelling: hot water heater

被引：0
|
作者：
Savatorova, Viktoria [1 ]
Talonov, Aleksei [2 ]
机构：
[1] Cent Connecticut State Univ, New Britain, CT 06050 USA
[2] Univ Nevada, Las Vegas, NV USA
来源：
INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY | 2024年 / 55卷 / 02期
关键词：
Mathematical modelling; ordinary differential equations; hot water heater;
D O I：
10.1080/0020739X.2023.2249899
中图分类号：
G40 [教育学];
学科分类号：
040101 ; 120403 ;
摘要：
We present an example of one of the modelling projects we assign to students in our differential equations classes. Students are asked to determine how to run a cost-efficient hot water heating system. We consider a cylindrical tank filled with water and heated by a heating element immersed in it. Together with students we discuss physical laws governing the process and make assumptions necessary to build a model. One of the goals of the modelling activity is to compute the time needed for water to reach the desired temperature given the power of the heating element and the size of the water tank. Several different scenarios can be discussed. Assuming the cost of heating the water is directly related to the time for which the power is ON, students can choose the most cost-efficient scenario. We provide the description of several modelling activities and obtained results.
引用
收藏
页码：235 / 263
页数：29
相关论文
共 50 条
  • [41] Exergetic optimization of a PEM fuel cell for domestic hot water heater
    Saidi, M. H.
    Abbassi, A.
    Ehyaei, M. A.
    JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY, 2005, 2 (04): : 284 - 289
  • [42] Domestic hot water pre-heater utitlizing solar energy
    Lovász, Anett
    Bajnóczy, Gábor
    Periodica Polytechnica Chemical Engineering, 2006, 50 (01) : 45 - 53
  • [43] CFD Analysis of Solar Hot Water Heater with Integrated Storage System
    Yahya, M.
    Sopian, K.
    Syahri, M.
    Abdullah, S.
    Alghoul, M. A.
    Zaharim, A.
    PROCEEDINGS OF THE 7TH WSEAS INTERNATIONAL CONFERENCE ON SYSTEM SCIENCE AND SIMULATION IN ENGINEERING (ICOSSSE '08): RECENT ADVANCES IN SYSTEMS SCIENCE AND SIMULATION IN ENGINEERING, 2008, : 323 - +
  • [44] Optimization of the Investment Effect for the Solar Hot-Water Heater in Taiwan
    Yu, Sun-Nien
    JOURNAL OF APPLIED SCIENCE AND ENGINEERING, 2009, 12 (04): : 391 - 397
  • [45] Analysis of a Fuel Cell Hot Water Heater for Combined Heat and Power
    Ghotkar, Rhushikesh
    Milcarek, Ryan J.
    ASHRAE TRANSACTIONS 2020, VOL 126, 2020, 126 : 23 - 25
  • [46] Teaching geomorphology through spreadsheet modelling
    Locke, WW
    GEOMORPHOLOGY, 1996, 16 (03) : 251 - 258
  • [47] TIC in the teaching of the first order differential equations
    Rincon Leal, Olga Lucy
    LOGOS CIENCIA & TECNOLOGIA, 2016, 8 (01): : 89 - 100
  • [48] Interactive Simulations for Teaching and Learning Differential Equations
    Magrez, Hamid
    Salmi, Khalid
    Ziyyat, Abdelhak
    2016 INTERNATIONAL CONFERENCE ON INFORMATION TECHNOLOGY FOR ORGANIZATIONS DEVELOPMENT (IT4OD), 2016,
  • [49] MODELLING SUPPLY NETWORKS WITH PARTIAL DIFFERENTIAL EQUATIONS
    D'Apice, C.
    Manzo, R.
    Piccoli, B.
    QUARTERLY OF APPLIED MATHEMATICS, 2009, 67 (03) : 419 - 440
  • [50] Editorial: Differential equations: Modelling and numerical methods
    Mohanty, R. K.
    Perfilieva, Irina
    Sharma, Kapil K.
    Cardone, Angelamaria
    Jha, Navnit
    METHODSX, 2023, 10
12345