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Numerical Solution of Axisymmetric Inverse Heat Conduction Problem by the Trefftz Method

Author

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  • Sylwia Hożejowska

    (Faculty of Management and Computer Modelling, Kielce University of Technology, 25-314 Kielce, Poland)

  • Magdalena Piasecka

    (Faculty of Mechatronics and Mechanical Engineering, Kielce University of Technology, 25-314 Kielce, Poland)

Abstract

In this paper, the issue of flow boiling heat transfer in an annular minigap was discussed. The main aim of the paper was determining the boiling heat transfer coefficient at the HFE-649 fluid–heater contact during flow along an annular minigap. The essential element of the experimental stand was a test section vertically oriented with the minigap 2 mm wide. Thermocouples were used to measure the temperature of the heater and fluid at the inlet and the outlet to the minigap. The mathematical model assumed that the fluid flow was laminar and the steady–state heat transfer process was axisymmetric. The temperatures of the heated surface and of the flowing fluid were assumed to fulfill energy equations with adequate boundary conditions. The problem was solved by the Trefftz method. The local heat transfer coefficients at the fluid–test surface interface were calculated due to the third kind boundary condition at the saturated boiling. Graphs were used to illustrate: the measurement of the heater surface temperature, 2D temperature distributions in the pipe and fluid, and the heat transfer coefficient as a function of the distance from the minigap inlet. The measurement uncertainties and accuracy of the heat transfer coefficient determination were estimated.

Suggested Citation

  • Sylwia Hożejowska & Magdalena Piasecka, 2020. "Numerical Solution of Axisymmetric Inverse Heat Conduction Problem by the Trefftz Method," Energies, MDPI, vol. 13(3), pages 1-14, February.
  • Handle: RePEc:gam:jeners:v:13:y:2020:i:3:p:705-:d:317250
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    References listed on IDEAS

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    1. Li, Qi & Flamant, Gilles & Yuan, Xigang & Neveu, Pierre & Luo, Lingai, 2011. "Compact heat exchangers: A review and future applications for a new generation of high temperature solar receivers," Renewable and Sustainable Energy Reviews, Elsevier, vol. 15(9), pages 4855-4875.
    2. Mirosław Grabowski & Sylwia Hożejowska & Anna Pawińska & Mieczysław E. Poniewski & Jacek Wernik, 2018. "Heat Transfer Coefficient Identification in Mini-Channel Flow Boiling with the Hybrid Picard–Trefftz Method," Energies, MDPI, vol. 11(8), pages 1-13, August.
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    Cited by:

    1. Magdalena Piasecka & Beata Maciejewska & Paweł Łabędzki, 2020. "Heat Transfer Coefficient Determination during FC-72 Flow in a Minichannel Heat Sink Using the Trefftz Functions and ADINA Software," Energies, MDPI, vol. 13(24), pages 1-25, December.
    2. Magdalena Piasecka & Sylwia Hożejowska & Anna Pawińska & Dariusz Strąk, 2022. "Heat Transfer Analysis of a Co-Current Heat Exchanger with Two Rectangular Mini-Channels," Energies, MDPI, vol. 15(4), pages 1-19, February.
    3. Dominika Babička Fialová & Zdeněk Jegla, 2021. "Experimentally Verified Flow Distribution Model for a Composite Modelling System," Energies, MDPI, vol. 14(6), pages 1-24, March.
    4. Magda Joachimiak, 2021. "Analysis of Thermodynamic Parameter Variability in a Chamber of a Furnace for Thermo-Chemical Treatment," Energies, MDPI, vol. 14(10), pages 1-18, May.
    5. Mohsen Tadi & Miloje Radenkovic, 2021. "Non-Iterative Solution Methods for Cauchy Problems for Laplace and Helmholtz Equation in Annulus Domain," Mathematics, MDPI, vol. 9(3), pages 1-14, January.
    6. Sun Kyoung Kim, 2021. "Influence of Errors in Known Constants and Boundary Conditions on Solutions of Inverse Heat Conduction Problem," Energies, MDPI, vol. 14(11), pages 1-20, June.
    7. Magdalena Piasecka & Sylwia Hożejowska & Beata Maciejewska & Anna Pawińska, 2021. "Time-Dependent Heat Transfer Calculations with Trefftz and Picard Methods for Flow Boiling in a Mini-Channel Heat Sink," Energies, MDPI, vol. 14(7), pages 1-24, March.

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