Numerical Simulation of Roughness in Microchannels by Using the Second-Order Slip Boundary Condition

A numerical scheme for simulation of flow in a microchannel was developed. The effect of channel roughness was directly considered by modeling various shapes of wall roughness using second-order slip boundary condition. Governing equations of compressible and incompressible flows with different Mach and Knudsen numbers were solved using the SIMPLE algorithm. Studying flows in smooth microchannels, unique slip and centerline velocities were found by applying either first- or second-order slip boundary condition, whereas in rough channels more reliable values were found by applying a second-order model. The same trend was observed for Poiseuille number and pressure gradient especially at higher Mach and Knudsen numbers.