Developing of laminar fluid flow in rectangular microchannels

Two dimensional elliptic differential equations are solved numerically to investigate laminar fluid flow in rectangular microchannels. The model employs the Navier-Stokes equations with velocity slip at the wall boundary condition to simulate the flow behavior in microchannels. The numerical solution is obtained by discretizing the governing equations using the finite-volume technique. A numerical code was developed. The developed code is used to evaluate the effects of velocity slip, the flow rate and size of microchannel on the fluid flow in rectangular microchannels. The numerical simulations are done on a wide range of the Reynolds number (Re), the Knudsen number (Kn) for three different values of the width of microchannel. The results shows good agreement with previous published experimental data. The effects of rarefaction and flow rate on the flow behavior and the hydrodynamic developing fluid field are presented and discussed. The developing profile of velocity and pressure due to different Re and Kn, are shown. It is found that at a given Re, increasing the Knudsen number causes to decrease the dimensionless pressure along the microchannel. An increasing in the Knudsen number reduces the maximum velocity in the microchannels while the entrance length increases at any Re.