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

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.