The book presents the first systematic exposition of the problem related to microfluid flow developing under conditions of intensive heat transfer and phase changing of working fluid. A wide class of the problem are concerned with drag and heat transfer in micro–channels at laminar and turbulent flows of single and two–phase fluids, effect of energy dissipation, axial conduction, wall roughness on flow characteristics, in particular, values of operating parameters, corresponding to stable and unstable states. Attention is paid to analysis of steady and unsteady capillary flow with distinct interface in the frame of unit approach is based on quasi–one–dimensional model accounting the affect of capillarity, frictional and gravity forces on the flow development. A number of specific problems are connected with effect of axial conduction, wall roughness, as well as optimization of micro–heat exchanger is considered. The correlation for calculating drag and heat transfer of micro–channels different geometry are presented.