Pressure Drop and Flow Development in the Entrance Region of Microchannels With Second-Order Velocity Slip Condition and the Requirement for Development Length

In this investigation, L-fd* and Delta p in the entrance region of circular and parallel plate microchannels have been determined for 10(-2) <= Re <= 10(4) and 10(-4) <= Kn <= 0.2, employing the second-order velocity slip condition at the wall with C-1 = 1 and 0 <= C-2 <= 0.5. Results indicate that although local velocity slip at the wall is always higher than that for the fully developed section, local wall shear stress for higher Kn and C-2 could be lower than its fully developed value, which is also more prominent for lower Re. Therefore, depending upon the operating condition, K(x) and K-fd could assume negative values, implying that pressure gradient in the developing region could even be less than that in the fully developed section. It has been further observed that both L-fd* and K-fd are characterized by the low and the high Re asymptotes, using which extremely accurate correlations have been proposed for both geometries.