The extended surfaces have fins attached to the primary surface on one side of a two-fluid or multi-fluid heat exchanger. The fins may be of a variety of geometries: smooth, corrugated or interrupted, and can be fixed to the interior, to the outside or to both sides of circular, flat or oval tubes, or separation sheets. The pins are mainly used to increase the surface area (when the heat transfer coefficient on that side of the fluid is relatively low) and, consequently, to increase the total heat transfer rate. In addition, improved fin geometries also increase the coefficient of heat transfer compared to that of a flat fin. The fins may also be used on the side of the high heat transfer coefficient fluid in a heat exchanger mainly for structural strength (eg for high pressure water flow through a flat tube) or to provide A deep mixing of a highly viscous liquid for the flow of laminar oil in a flat or round tube). The fins are attached to the primary surface by brazing, welding, adhesive bonding or mechanical expansion, or are extruded or integrally connected to the tubes.