Tube heat exchanger comprising finned tubes, wherein the tubes extend in a certain axial direction and are provided with heat exchange fins. Each fin has a heat exchange surface surrounding a tube that extends in a certain radial direction in relation to the tube and which is relief structured to form grooves spaced apart from one another in said radial direction. The grooves of a fin have different dimensions that decrease on moving away from the tube in said radial direction so as to form a guide for a fluid around the tube.