Trefftz Method for Time-Dependent Boiling Heat Transfer Calculations in a Mini-Channel Utilising Various Spatial Orientations of the Flow

Magdalena Piasecka, Sylwia Hożejowska, Artur Maciąg () and Anna Pawińska
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Magdalena Piasecka: Faculty of Mechatronics and Mechanical Engineering, Kielce University of Technology, Al. Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland
Sylwia Hożejowska: Faculty of Management and Computer Modelling, Kielce University of Technology, Al. Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland
Artur Maciąg: Faculty of Management and Computer Modelling, Kielce University of Technology, Al. Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland
Anna Pawińska: Faculty of Management and Computer Modelling, Kielce University of Technology, Al. Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland

Energies, 2025, vol. 18, issue 17, 1-23

Abstract: The main objective of this study was to investigate boiling heat transfer during refrigerant flow in a mini-channel heat sink. The test section consisted of multiple parallel mini-channels, each with a depth of 1 mm. The working fluid was heated by a thin layer of Haynes-230 alloy with a thickness of 0.1 mm. The outer surface temperature of the heater was measured using infrared thermography, while other thermal and flow-based parameters were recorded via a dedicated data acquisition system. The mini-channel heat sink was tested in seven different spatial orientations, with inclination angles relative to the horizontal plane of 45°, 60°, 75°, 90°, 105°, 120°, and 135°. The analysis focused on the early stage of the experiment, corresponding to the forced convection, boiling incipience, and subcooled boiling region. A time-dependent, two-dimensional model of heat transfer during flow boiling of a refrigerant in asymmetrically heated mini-channels was developed. The temperatures of both the heating foil and the working fluid (Fluorinert FC-770) were described using appropriate forms of the Fourier–Kirchhoff equation, subject to relevant boundary conditions. Two sets of time-dependent Trefftz functions were employed to solve the governing equations: one set corresponding to the two-dimensional Fourier equation and another, newly derived, for the energy equation in the fluid. The results include thermographic images of the heated surface, temperature distributions, fluid temperatures, local heat-transfer coefficients, and boiling curves. A comparison of the heat-transfer coefficients obtained using the Trefftz-based approach and those calculated using Fourier’s law demonstrated satisfactory agreement.

Keywords: flow boiling; heat transfer coefficient; mini-channel; inverse problem; time-dependent; Trefftz method (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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