An extended numerical analysis is performed in order to characterize the combined effect of compressibility, rarefaction and conjugate heat transfer (CHT) in counter current and parallel flow micro heat exchanger. Relatively short microchannel geometries are considered, leading to more significant dependence on compressibility and rarefaction effects. A fully compressible numerical solver, coupled with proper slip flow and temperature jump boundary conditions, previously extensively used for CHT computation in microchannel heat sinks, is adopted: thus, viscous dissipation is always taken into account and a wide range of channel exit Mach numbers can be considered, keeping Knudsen number within the limits of slip flow. A comprehensive range of fluid/solid thermal conductivity ratios, pressure ratios, temperature difference and channel aspect ratios are considered, in order to identify the dominant effects, as well as the optimal fluid/solid conductivity ratio, as a function of the heat exchanger design and operating parameters. Results are described in terms of heat exchanger efficiency and local Nusselt number
