IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v468y2024ics0096300323006938.html
   My bibliography  Save this article

Relationship between two solidification problems in order to determine unknown thermal coefficients when the heat transfer coefficient is very large

Author

Listed:
  • Salva, N.N.
  • Tarzia, D.A.

Abstract

The phase-change processes are found in a wide variety of dynamic systems, for example in the study of snow avalanches. When a thermal property of the material is unknown, we can add a boundary condition to formulate an Inverse Stefan Problem, and determine this property. In this paper we study a heat conduction phase-change problem with Robin and Neumann boundary condition at a fixed face. This overspecified condition allows to simultaneously determine two unknown thermal coefficients through a moving boundary problem or a free boundary problem. Formulae for different cases where obtained by Ceretani and Tarzia (2015) [6]. The formulation with these type of boundary conditions is a more realistic one than the heat conduction phase-change problems with Dirichlet and Neumann boundary condition at the fixed face, considered by Tarzia, (1982-1983). Therefore we propose to study the relationship between the problems with Robin-Neumann conditions, and the problems with Dirichlet-Neumann conditions. The main result of this work is the convergence analysis of these problems, when the heat transfer coefficient h of the Robin condition is very large. We present for each case of the free and moving boundary problems, an upper bound for the error of the two unknown parameters, obtaining in every case a bound of order o(1h). Finally we show a numerical example of the convergence, for a phase change material commonly used in heating or cooling processes.

Suggested Citation

  • Salva, N.N. & Tarzia, D.A., 2024. "Relationship between two solidification problems in order to determine unknown thermal coefficients when the heat transfer coefficient is very large," Applied Mathematics and Computation, Elsevier, vol. 468(C).
    • Handle: RePEc:eee:apmaco:v:468:y:2024:i:c:s0096300323006938
    DOI: 10.1016/j.amc.2023.128524
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323006938
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128524?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhou, D. & Zhao, C.Y. & Tian, Y., 2012. "Review on thermal energy storage with phase change materials (PCMs) in building applications," Applied Energy, Elsevier, vol. 92(C), pages 593-605.
    2. Yu, Yue & Xu, Dinghua, 2015. "On the inverse problem of thermal conductivity determination in nonlinear heat and moisture transfer model within textiles," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 284-299.
    3. Barret L. Kurylyk & Masaki Hayashi, 2016. "Improved Stefan Equation Correction Factors to Accommodate Sensible Heat Storage during Soil Freezing or Thawing," Permafrost and Periglacial Processes, John Wiley & Sons, vol. 27(2), pages 189-203, April.
    4. Andrea N. Ceretani & Domingo A. Tarzia, 2015. "Determination of One Unknown Thermal Coefficient through a Mushy Zone Model with a Convective Overspecified Boundary Condition," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, October.
    5. Huntul, M.J. & Lesnic, D. & Hussein, M.S., 2017. "Reconstruction of time-dependent coefficients from heat moments," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 233-253.
    6. Gaudiano, Marcos & Torres, Germán Ariel & Turner, Cristina, 2009. "On a convective condition in the diffusion of a solvent into a polymer with non-constant conductivity coefficient," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 479-489.
    7. Alpar, Sultan & Rysbaiuly, Bolatbek, 2023. "Determination of thermophysical characteristics in a nonlinear inverse heat transfer problem," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ceretani, Andrea N. & Salva, Natalia N. & Tarzia, Domingo A., 2018. "Approximation of the modified error function," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 607-617.
    2. Gholamibozanjani, Gohar & Farid, Mohammed, 2020. "A comparison between passive and active PCM systems applied to buildings," Renewable Energy, Elsevier, vol. 162(C), pages 112-123.
    3. Jiang, Fuyun & Wang, Xiaodong & Wu, Dezhen, 2016. "Magnetic microencapsulated phase change materials with an organo-silica shell: Design, synthesis and application for electromagnetic shielding and thermal regulating polyimide films," Energy, Elsevier, vol. 98(C), pages 225-239.
    4. Nie, Binjian & She, Xiaohui & Du, Zheng & Xie, Chunping & Li, Yongliang & He, Zhubing & Ding, Yulong, 2019. "System performance and economic assessment of a thermal energy storage based air-conditioning unit for transport applications," Applied Energy, Elsevier, vol. 251(C), pages 1-1.
    5. Shahsavar, Amin & Al-Rashed, Abdullah A.A.A. & Entezari, Sajad & Sardari, Pouyan Talebizadeh, 2019. "Melting and solidification characteristics of a double-pipe latent heat storage system with sinusoidal wavy channels embedded in a porous medium," Energy, Elsevier, vol. 171(C), pages 751-769.
    6. Xu, Biwan & Ma, Hongyan & Lu, Zeyu & Li, Zongjin, 2015. "Paraffin/expanded vermiculite composite phase change material as aggregate for developing lightweight thermal energy storage cement-based composites," Applied Energy, Elsevier, vol. 160(C), pages 358-367.
    7. Wang, Yunming & Tang, Bingtao & Zhang, Shufen, 2014. "Organic, cross-linking, and shape-stabilized solar thermal energy storage materials: A reversible phase transition driven by broadband visible light," Applied Energy, Elsevier, vol. 113(C), pages 59-66.
    8. Lei, Jiawei & Yang, Jinglei & Yang, En-Hua, 2016. "Energy performance of building envelopes integrated with phase change materials for cooling load reduction in tropical Singapore," Applied Energy, Elsevier, vol. 162(C), pages 207-217.
    9. Jaworski, Maciej & Łapka, Piotr & Furmański, Piotr, 2014. "Numerical modelling and experimental studies of thermal behaviour of building integrated thermal energy storage unit in a form of a ceiling panel," Applied Energy, Elsevier, vol. 113(C), pages 548-557.
    10. Kensby, Johan & Trüschel, Anders & Dalenbäck, Jan-Olof, 2015. "Potential of residential buildings as thermal energy storage in district heating systems – Results from a pilot test," Applied Energy, Elsevier, vol. 137(C), pages 773-781.
    11. Sun, Xiaoqin & Medina, Mario A. & Lee, Kyoung Ok & Jin, Xing, 2018. "Laboratory assessment of residential building walls containing pipe-encapsulated phase change materials for thermal management," Energy, Elsevier, vol. 163(C), pages 383-391.
    12. Alvi, Jahan Zeb & Feng, Yongqiang & Wang, Qian & Imran, Muhammad & Pei, Gang, 2021. "Effect of phase change materials on the performance of direct vapor generation solar organic Rankine cycle system," Energy, Elsevier, vol. 223(C).
    13. Pitié, F. & Zhao, C.Y. & Baeyens, J. & Degrève, J. & Zhang, H.L., 2013. "Circulating fluidized bed heat recovery/storage and its potential to use coated phase-change-material (PCM) particles," Applied Energy, Elsevier, vol. 109(C), pages 505-513.
    14. Cong Zhou & Yizhen Li & Fenghao Wang & Zeyuan Wang & Qing Xia & Yuping Zhang & Jun Liu & Boyang Liu & Wanlong Cai, 2023. "A Review of the Performance Improvement Methods of Phase Change Materials: Application for the Heat Pump Heating System," Energies, MDPI, vol. 16(6), pages 1-21, March.
    15. Abdelkader Sarri & Saleh Nasser Al-Saadi & Müslüm Arıcı & Djamel Bechki & Hamza Bouguettaia, 2023. "Architectural Design Strategies for Enhancement of Thermal and Energy Performance of PCMs-Embedded Envelope System for an Office Building in a Typical Arid Saharan Climate," Sustainability, MDPI, vol. 15(2), pages 1-29, January.
    16. Sun, Xiaoqin & Zhang, Quan & Medina, Mario A. & Liao, Shuguang, 2015. "Performance of a free-air cooling system for telecommunications base stations using phase change materials (PCMs): In-situ tests," Applied Energy, Elsevier, vol. 147(C), pages 325-334.
    17. Neda Hajibandeh & Mehdi Ehsan & Soodabeh Soleymani & Miadreza Shafie-khah & João P. S. Catalão, 2017. "The Mutual Impact of Demand Response Programs and Renewable Energies: A Survey," Energies, MDPI, vol. 10(9), pages 1-18, September.
    18. Yu, Jinghua & Leng, Kangxin & Ye, Hong & Xu, Xinhua & Luo, Yongqiang & Wang, Jinbo & Yang, Xie & Yang, Qingchen & Gang, Wenjie, 2020. "Study on thermal insulation characteristics and optimized design of pipe-embedded ventilation roof with outer-layer shape-stabilized PCM in different climate zones," Renewable Energy, Elsevier, vol. 147(P1), pages 1609-1622.
    19. Rostami, Sara & Afrand, Masoud & Shahsavar, Amin & Sheikholeslami, M. & Kalbasi, Rasool & Aghakhani, Saeed & Shadloo, Mostafa Safdari & Oztop, Hakan F., 2020. "A review of melting and freezing processes of PCM/nano-PCM and their application in energy storage," Energy, Elsevier, vol. 211(C).
    20. Ahmed Hassan & Mohammad Shakeel Laghari & Yasir Rashid, 2016. "Micro-Encapsulated Phase Change Materials: A Review of Encapsulation, Safety and Thermal Characteristics," Sustainability, MDPI, vol. 8(10), pages 1-32, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:468:y:2024:i:c:s0096300323006938. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.