Numerical Investigation to Derive Correlations for Hydrodynamic Entrance Length in Very Low Reynolds Number Regime in Rectangular Microchannels

Abstract

A three-dimensional laminar flow model was used for 37 Reynolds numbers (0.1, 0.2…1, 2…10, 20…100, and 200…1000) through six rectangular microchannels (aspect ratios: 1, 0.75, 0.5, 0.25, 0.2, and 0.125) to develop correlations for hydrodynamic entrance length. The majority of the Reynolds numbers are in the low regime (Re < 100) to fulfill the need to determine the hydrodynamic entrance length for microchannels. Examination of the fully developed flow condition was considered using the velocity or fRe criteria. Numerical results from the present simulations were validated by comparing the fRe results. Two new correlations were developed from a vast amount of numerical data (222 simulations). The velocity criterion correlations predict entrance length with a mean error of 4.67% and maximum error of 10.28%. The fRe criterion generated better correlations and were developed as a function of aspect ratio to predict entrance length with a mean error less than 2% and maximum error of 5.75% for 0.1 ≤ Re ≤ 1000 and 0 ≤ α ≤ ∞.