PURPOSE: A fluid mixing unit is provided to be able to quickly and exactly mix two kinds of fluids without an extra agitating device by a screw inside a square vessel. CONSTITUTION: The heat exchanging unit comprises:a circumferential space(2) formed inside the square vessel; a recessed groove group(4) formed in the circumferential wall(3); a screw(5) inputted inside the circumferential space(2); a spiral passage(7) by agreeing a screw hill(6) with a spiral of the recessed groove group(4); a mixing inlet pipe and a draining pipe(9) equipped in the both ends.