Wall roughness and viscous dissipation effects in microchannel heat sinks with semicircular cross-section

A statistical analysis of the wall roughness effect is carried out to determine the impact of the shape uncertainty on the Poiseuille number and Nusselt number of laminar forced convection. The focus is on the fully developed regime in a semicircular microchannel where the heat transfer occurs from the diametrical plane boundary, modelled as a perfectly smooth surface. On the other hand, the curved semicircular boundary is devised as rough and with a negligible wall heat flux. Three types of thermal boundary conditions are implemented: the T condition, the H1 condition and the H2 condition. The T condition serves to model a case where the fluid temperature does not undergo any change in the streamwise direction, while the H1 and H2 conditions are employed to describe a net heating of the fluid. A statistical sample of several different rough microchannels is used to detect the actual effects of roughness on the Poiseuille number and on the Nusselt number, through the evaluation of their average values and standard deviations. The governing local momentum and energy balance equations are solved numerically by a finite element method taking into account the viscous dissipation contribution to the local energy balance.