An apparatus for the mixing conveying of fluids with heat exchange includes a housing with installations that each include a first hollow structure for conveying a first fluid while a second fluid is able to flow around the first hollow structure. The second fluid flows along a main flow direction which is substantially disposed along the longitudinal axis of the housing. A second hollow structure is provided through which the first fluid can flow and which can be flowed around by the second fluid with the second hollow structure being arranged cross-wise with respect to the first hollow structure. The hollow structures have a flow cross-section with a first width B1 and a second width B2, with B1/B2 being larger than one and B1 oriented normally to a plane which contains the longitudinal axis of the housing or a line parallel to the longitudinal axis and an axis of the hollow structure.