Abstract: Device suitable for use in heat and mass transfer applications comprising a manifold structure having outwardly extending protrusions from the surface thereof and which is spirally wound into a plurality of convolutions and is surrounded by a shell having a cylindrical body member and conical ends. The protrusions are interconnected with one another so that flow progresses from one to another. The device can be used for heat transfer and for mass transfer between various fluid streams, in particular, venous blood and a stream of oxygen. The manifold structure being spirally wound provides a manifold for oxygen flow in an axial, as well as circumferential, direction. Blood flows axially through the mass transfer device in a plurality of essentially concentric streams. When two manifold structures are provided in tandem in a body member, both heat and mass transfer can be provided with a stream of blood.