When mixing augmentation is not available, heat can be transported across micro-channels by conduction only. A method to increase this heat flow has been proposed. The method relies on the use of grooves parallel to the flow direction. It has been shown that it is possible to find grooves that can increase the heat flow and, at the same, can decrease the flow pressure losses. The optimal groove shape that maximizes the overall system performance has been determined. (C) 2013 Elsevier Ltd. All rights reserved.