A hybrid solver dynamically coupling the kinetic solution computed in local rarefied areas and the Navier-Stokes solution in the rest of the flow is used for the investigation of heat transfer in microchannels with rough wall surfaces. Roughness is modeled as a series of triangular obstructions with a relative roughness height from 0 up to 5% of the channel height. A nearly incompressible gas flow (low Mach number) for a range of Knudsen numbers from 0.01 up to 0.1 is considered. The competition between roughness, rarefaction and heat transfer effects is discussed in terms of average Nusselt and Poiseuille numbers and mass flow rate. The discrepancy between the full Navier-Stokes and hybrid solutions is analyzed, assessing the range of applicability of the first order slip boundary condition for rough geometries in the presence of heat transfer
