Nusselt number and development length correlations for laminar flows of water and air in microchannels

Computational Fluid Dynamics (CFD) analyses are carried out to investigate convective heat transfer of developing laminar flows of water and air in microchannels, for wide ranges of parameters (alpha = 1-10, D-h = 145-375 mu m, L/D-h = 130-750, Q= 1-18 W, Pr-in = 0.7-11.2, and Re-in = 130-900). The convergence of the results validated the numerical approach and the mesh grid refinement used and the accuracy is confirmed by the excellent comparison to reported experimental results. The results account for the azimuthal variations of the wall heat flux and temperature, and the changes of the fluid properties with temperature along the microchannel. The compiled database from the present analyses results are used to correlate the local Nu(ch)(z), which is integrated along the microchannel length to obtain the average Nusselt number, (Nu) over bar (ch). A continuous correlation of (Nu) over bar (ch), is developed in terms of Nusselt number for fully developed flow Nu(fd), Re-in, alpha, and Pr-in, as: (Nu) over bar (ch) = Nu(fd) [1.0 + 0.0363/L*(0.631)], Nu(fd) = 8.235 - (17.2/(3.785 + (alpha - 1)(1.11))), and L* = [(L/D-h)(alpha(0.583)/(ReinPrin))](1.2) The values of the thermal development length, iota(th), for Nu(ch)(z) are also correlated in terms of D-h, alpha, Re-in, and Pr-in, as: iota(th) = (0.028 + 0.088e(-0.45(alpha-1)))DhReinPrin The correlations of Nu(ch)(z), (Nu) over bar (ch) and iota(th) are in excellent agreement with the present numerical results and those reported by other investigators for Nuch(z) and (Nu) over bar (ch). The numerical values of (Nu) over bar Nu(ch), are 10-20% higher than those reported experimentally, assuming uniform wall and fluid temperatures along the microchannel, and neglecting the effects of the flow development and the azimuthal variations in the wall heat flux and temperature. (C) 2018 Elsevier Ltd. All rights reserved.