Correlation between heat transfer and pressure drop in channels with periodically grooved parts along the streamwise direction is investigated for various channel configurations by assuming two-dimensional and periodically fully developed flow and temperature fields, Streamwise periodic variations of the cross-section induce the bifurcation from steady-state flow to oscillatory one. Heat transfer is enhanced significantly after the bifurcation with the increase of pressure drop. An efficiency defined as the ratio of the heat transfer enhancement to the increase of pressure drop is considered. It is found that the channels with expanded grooves perform efficiently, while the channels with contracted grooves inefficiently.