The Effect of Random Roughness for Fully Developed Forced Flow in Square Microchannels

The role of wall roughness in heat and mass transfer for fully developed viscous flows in square microchannels is investigated here. Since the roughness, which is the key geometrical feature to be investigated, introduces high velocity gradients at the wall, the effect of the viscous dissipation is considered. A fully developed flow in the forced convection regime is assumed. This assumption allows the two-dimensional treatment of the problem; thus, the velocity and temperature fields are simulated on the microchannel cross-section. The boundary roughness is modeled by randomly throwing points around the nominal square cross-section perimeter and by connecting those points to generate a simple polygon. This modification of the nominal square shape of the cross-section influences the velocity and temperature fields, which are computed by employing a finite element method solver. The heat and mass transfer is studied by calculating the Nusselt and the Poiseuille numbers as a function of roughness amplitude at the boundary. Each Nusselt and Poiseuille number is obtained by employing an averaging procedure over a sample of a thousand cases.