A tube heat exchanger for exchanging heat from a first fluid to a second fluid, comprising a tubular shell; an inner wall extending around a center axis of said tubular shell and forming a central chamber internally of said inner wall, and an annular heat exchange space extending externally of said inner wall and enclosed by said tubular shell, wherein the heat exchange space comprises a plurality of axially extending heat exchange sectors separated by radially extending separating walls, and flow paths of the first fluid and the second fluid extend in the heat exchange space, wherein adjacent heat exchange sectors communicate; and a set of flow tubes extending axially in each of said heat exchange sectors in said heat exchange space. At least one radially extending baffle is provided to divide said heat exchange sectors into at least two axially displaced heat exchange segments, wherein a flow path of the second fluid extends radially in opposite directions in adjacent heat exchange segments in the heat exchange sectors, and a flow path of the first fluid extends perpendicular to the flow path of the second fluid.