In the present work the effect of surface roughness on laminar fluid flow in micro channels has been studied. According to value of the Knudsen number(0.1 Kn 0.01)continuum hypothesis is feasible and slip boundary condition is assumed. The Navier Stokes equations are solved numerically with the finite element method. According to the flow Mach number (Ma 0.3) and negligible temperature variation along the short length of the channel, incompressible fluid with constant density is assumed. Air is the working fluid inside the channel. Analytical and numerical results for velocity and poiseuille number of smooth channel have been compared and the error was less than 1% wich is acceptable. Roughness is modeled as a series of alternating barriers with triangular base geometry on two-dimensional channel walls. The effect of roughness height variation from one to six percent of channel height is examined. The roughness element bottom width variation from one to thirty times of roughness height is examined too. Also the distance variation between roughness elements from zero to about eight times of roughness width is examined. The roughness element top width variation from zero to a value equal to roughness bottom width is examined. These effects were studied on the slip and poiseuille number. Also the effect of varying roughness geometry from two dimensional to three dimensional is studied.The results show that prediction of slip and poiseuille number would have almost 100% and 27% errors respectively with variations of roughness parameters in a certain knudsen number. The result of all channels are studied and compared in the locally developed part of the flow. For a number of studied channels the Poiseuille number of developed parts have been compared with the developing part and about 38% error has been achieved. Many of real surfaces elements can be approximated with triangular elements, so we can predict these cases with the presents works result. But the real elements have different ratio of bottom width to height roughness elements, even in a one surface, so we should determine the average value of height and width and then according to this values, slip and poiseuille number are achieved from the present works result. The slip and poiseuille number prediction of some real surfaces are compared with the result of the numerical solution of these surfaces and utmost 10% error is achieved. Keywords Micro Channel, Roughness, Slip, Pressure Drop, Poiseuille, Knudsen.
