Trefftz function-based thermal solution of inverse problem in unsteady-state flow boiling heat transfer in a minichannel

The paper shows the results for flow boiling heat transfer in a 1.7 mm deep minichannel vertically oriented with FC-72 Fluorinert as a working fluid. The heated wall of the minichannel was formed with a thin foil. Thermocouples mounted at 18 points monitored the outer foil surface temperature. All experimental parameters were controlled using data acquisition stations. The measurements were performed at 0.01 s intervals. The observations of the flow structures were carried out concurrently on the internal surface of the foil contacting the fluid. The aim of the numerical calculations was to determine the heat transfer coefficient on the contact surface between the heated foil and FC-72. The heat transfer coefficient was calculated with the use of the Robin boundary condition. To do that, the foil and fluid temperatures and foil temperature gradient had to be known. The foil temperature was found by solving an unsteady-state two-dimensional inverse boundary problem with the use of the Trefftz method in time-space subdomains. A linear combination of Trefftz functions was used to approximate the foil temperature. The unknown coefficients of the Trefftz function linear combination were determined by minimizing the functional. Error propagation in time and mean relative differences determined between the measured and computed heated foil temperatures were presented.