The invention relates to an apparatus for influencing the outflow region of a tube carrier plate of a tube bundle heat exchanger, in particular for the food and beverage industry, and in this case in particular for temperature-sensitive and/or viscous food products in the dairy industry, for example desserts, sauces or concentrates, according to the preamble of claim 1. The object of the present invention is to develop an apparatus of the generic type in such a way that the tendency for deposits to form in the region of the tube carrier plate through which a product has flowed out is considerably reduced. This is achieved in that the annular space-like outlet channel (600d) has, at least overall in the region thereof between a maximum outside diameter (dmax) of the outlet-side displacement body (12) and the second connection opening (600a), a channel passage cross section (As) which has a constant passage cross section over the entire length of the defined region and which, in this region, corresponds to a total passage cross section (NAi) of all of the inner tubes (300), through which a product flows in parallel, of the number (N), which inner tubes each have an individual passage cross section (Ai) (figure 2).