The effect of roughness elements on heat transfer in fluids is different from their effect in gases because of the different thermal resistance of the viscous sublayer. The distinctive feature of the process was examined in every detail and generalised by two rules deduced, one for fluids with Pr > 5 and another for gases. For fluids, small equally dispersed roughness elements can disturb the viscous sublayer sufficiently. For gases, the enhancement is reached by creation of many reattachment zones after obstacles. Two- to three-fold heat transfer enhancement within the limits of Reynolds analogy 2St/c(f) is attainable.