Abstract: A heat exchanger having an outer shell which is long as compared with its diameter and having a helical double-walled finned volute member which is wound to a small diameter around a core member, the proportions being such that the fins on the double-walled member touch the core on the inside of the wound convolutions and touch the shell on the outside of the wound convolutions. The tube which comprises the outer wall of the double-walled member extends through the shell so that any leakage into the space between the inner and outer tubes of the double-walled tube member will be discharged outside of the shell. The process by which the exchanger is made includes the steps of inserting an inner tube in a length of finned outer tube, winding them into a volute member, inserting a central core member therein, installing these members in a shell member and spinning the shell member closed to seal with the ends of the outer tubing of the volute member.