New Apparent Friction Factor Correlations for Developing and Fully Developed Laminar Flows in Rectangular Microchannels Via CFD Modeling

Abstract A three-dimensional laminar flow for 37 Reynolds numbers, primarily in low Reynolds number regime with water flow through six rectangular microchannels have been modeled conducting 222 simulations to develop correlations for fully developed friction factor and incremental pressure drop number to determine apparent fRe. Results from the present simulations were validated by comparing the fully developed velocity profile, friction factor, and incremental pressure drop number for Re > 100 in rectangular channels reported in the literature. Three new correlations were created from a vast array of numerical data generated from these simulations. First, a new fRe correlation was developed to include all aspect ratios, with a mean and maximum deviation of 0.14% and 0.26%, respectively, from the numerical results. Next, a correlation for the fully developed incremental pressure drop number, K(∞), was developed as a function of aspect ratio and Reynolds number. This correlation was in good agreement with the numerical data, with a mean deviation of 1.75% and a maximum deviation of 4.99%. The final correlation developed was for the incremental pressure drop number, K(z), in the developing region as a function of the non-dimensional axial distance, the aspect ratio, and the Reynolds number. The correlation was in good agreement with the numerical data, with a mean deviation of 0.80% and a maximum deviation of 5.93%. The local fapp,zRe, can be determined using the three correlations, with a maximum deviation of 8.23%, compared with the numerical results.