Research on the Equivalent Fin Method for experimental measurement of local Nusselt number in a one-sided heated rectangular channel

One-sided heated rectangular channels are commonly found in liquid cooling systems for heat-generating components such as semiconductors and battery packs. The non-uniform temperature distribution along the wetted perimeter makes it challenging to obtain the local Nusselt number ( Nu ) directly from experiments, because multiple measurement points would be required for averaging. To reduce this complexity, an Equivalent Fin Method (EFM) is proposed that inversely determines the local Nu from only two surface temperatures—the midpoints of the heated side and the opposite side—measured along the outer contour of the channel cross-section. Based on the aforementioned application conditions, 15 combinations of inlet Reynolds number, heat flux on the heated surface, and rectangular cross-section aspect ratio were selected, ranging from 3034 to 21,670, 10 to 60 W/cm 2 , and 0.5 to 3.0, respectively. A temperature-field dataset was obtained through simulations at nine axially equidistant positions in the heated section of a horizontal rectangular single channel. The EFM was established by correcting the inverted results using reference values obtained from the wetted-perimeter-averaged temperature method, and it was validated through scanning electron beam heating experiments. After correction, the deviation between the corrected inverse results and the simulation benchmark is reduced to −0.7%–0.9%. In the experiment-based verification, the maximum relative deviation between Nu EFM obtained from measured surface temperatures and the benchmark Nu from the validated simulation model is 7.5%. A turbulent heat-transfer correlation was obtained via least-squares regression using 495 simulation points, yielding R 2 = 0.9975. The proposed EFM enables practical measurement of local Nu and facilitates the development of heat-transfer correlations for one-sided heated rectangular channels.