Abstract: The invention relates to a connecting device having a female part and a complementary male part, wherein the female part is a sleeve able to receive at least partially the associated male part with a gap between the sleeve and the male part for receiving a brazing material. The sleeve at least partially has a conical shape. The conical shape has a first substantially conical part having a complementary shape to the male part, with a first inclination angle with respect to a longitudinal axis of the sleeve. The conical shape also has a second substantially conical part with a second inclination angle with respect to the axis, with the second inclination angle being larger than the first inclination angle.