then flows in the longitudinal direction 15 of the heat exchanger 12 to the lower level outlet end 16 of the same the condensate also entrains the accompanying substances separated out from the humid waste air in which case the condensate together with the accompanying substances after dropping from the oblique lower longitudinal edges 21 of the upright heat exchanger plates 13 flows along the oblique base 26 of the housing 14 of the heat exchanger 12 to the outlet end 16 of the heat exchanger 12 the condensate with the accompanying substances collecting on the base 26 upstream of the outlet end 16 of the housing 14 is directed out of the housing 14 in the region of the outlet end 16 of the heat exchanger 12 through the condensate connection 19 at the lower level bottom end of the base 26 the heat exchanger 12 is thus continuously freed from the condensate with the accompanying substances which in particular are bound in the condensate the condensate with the accompanying substances can then be directed away to an outflow for example a waste water channel it is also conceivable however for the condensate to be filtered that is to say outside the heat exchanger 12 for the condensate to have the accompanying substances at least some accompanying substances such as fluff removed from it and for the liquid condensate which is then freed at least for the most part from accompanying substances.