On Correlating Experimental Pressure Flow And Heat Transfer Measurements From Silicon Microchannels With Theoretical Calculations Cormac EasonNiall O’KeeffeRyan EnrightTara Dalton Stokes Research Institute, University of Limerick, Co. Limerick, Ireland

Causes Of Inconsistencies Electric double layer Loss of the continuum assumption validity due to small length scales Fluid property changes along the channel Inherent difficulties in taking measurements from flows at microscale High uncertainties in results derived from experimental measurements

Micro Scale Friction Factors Steinke and Kandlikar (2006) compiled 220 sets of data for single phase flow in microchannels between 1 and 1200 µm in diameter and reported experimental data varying over approximately an order of magnitude around theoretical laminar flow values Garimella (2006) also plotted pressure flow data from microchannels from several researchers, showing the same trend of inconsistency in friction factors from paper to paper

Micro Scale Friction Factors Steinke and KandlikarGarimella

Micro Scale Heat Transfer Garimella (2006) plots a drastic variation in Reynolds number Nusselt number correlations measured from microchannels over the past 15 years Bavière et al (2006) measured heat transfer from a parallel plate channel, accounting for variation in the channel surface temperature along the channel allowed the measured data to correlate with conventional heat transfer laws in laminar and turbulent regimes Numerical simulation of heat transfer has produced good correlation with experimental data in work by Lee and Garimella (2006), and Tiselj et al (2004), indicating that while standard correlations may not work, numerical simulation can correlate well with experimental data for specific test systems

Micro Scale Heat Transfer

Flow Loop Layout

Detail of Manifold Arrangement Thermocouple Locations in Each Manifold 

Experimental Ranges and Uncertainties Percent Uncertainty DRIEKOH

Channel Area Measurement

Channel Dimensions D h (µm) A (µm) DRIE KOH

Theoretical Pressure Drop Area Compensation Eason (2005) (Darcy’s Equation)

Friction Factors for Rectangular Channels Rohsenhow (1985)

Trapezoidal Channel Correlation Rohsenhow (1985)

Rectangular Channel Nu Correlations These correlations are also used to predict the heat transfer from the inlet and exit manifolds allowing this effect to be subtracted from the experimental data Schmidt (1985)

Muzychka and Yovanovich Correlation (2004)

Muzychka and Yovanovich Correlation

Manifold Entrance and Exit Losses Manifold friction losses are calculated using Darcy’s Equation as described earlier A M is the manifold flow area divided by the number of channels (22 for this work) Rohsenhow (1985)

Results

y=0.0315x R 2 = y=0.029x R 2 =0.9998

Suitable Correlations?

Results

Conclusions The fRe values from the system are less than predicted by both developing and fully developed theory. Though the DRIE channel data does not show an experimentally significant deviation from theory, this deviation is still unexpected as previous pressure flow work on similar channels correlated extremely well with theory The limited depth of field of the optical microscope used in measuring the channels may have caused unforseen errors in measuring the channels compared to previous SEM measurements Accounting for the effect of manifold heating on the heat transfer from the channel is essential to the correct interpretation of the data from the system The Nusselt number measured for this work shows a strong linear dependence on the Reynolds number but is not matched very closely by available correlations Numerical simulation of the test system will be performed in order to conclude as to the validity of the Nusselt number data

Questions?

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