On correlating experimental pressure flow and heat transfer measurements from silicon microchannels with theoretical calculations

The bulk pressure flow and heat transfer characteristics of rectangular and trapezoidal microchannels etched in silicon were measured in the laminar regime. The channel hydraulic diameters were 305 μm for the Deep Reactive Ion Etched (DRIE) etched channel and 317 μm for the wet etched channel and there were 22 channels in each sample. The fluid used was purified degassed water. The inlet and outlet temperature and pressure of the fluid and the wall temperatures of the channels were measured at the inlet and outlet of the channels. Theoretical and experimental results were calculated using fluid properties at the mean fluid temperature for each data point. These were then collapsed to a single curve at constant temperature by multiplying the measured value by the ratio of the relevant fluid properties at the experimental and required temperatures. The cross section of each channel on each channel sample was measured along with the channel height and width to give an area ratio between the actual channel width and the width calculated assuming the channel was perfectly rectangular or trapezoidal. This ratio is used to compensate the theoretical results and improve their correlation with the experiment. The uncertainty in the experimental results was calculated by running the result processing calculations three times, once at nominal values and then shifting input values to their upper and lower limits based on a 95% confidence interval on the standard deviation for each inputted measurement. Theoretical calculations were run for each experimental mass flow rate in order to produce equivalent theoretical points to the experimental values. Uncertainty in the theory is also determined by running the theoretical calculations at upper, lower and nominal 95% confidence interval values for the channels being tested. It was found that while the pressure flow data from the channels matched theoretical trends and that the results for the rectangular DRIE channels showed no experimentally significant deviation from theory, the experimental data from the wet etched trapezoidal channels was lower than predictions. The heat transfer from the channels is strongly affected by the heat transferred to the coolant by the manifolds. When this effect is removed, the experimental Reynolds number Nusselt number plot becomes strongly linear. This does not agree with theoretical predictions.