Evaporator with cool storage function

An evaporator with a cool storage function, the evaporator comprising:

• a plurality of flat refrigerant flow tubes having a longitudinal direction and a width direction which is perpendicular to the longitudinal direction and along which air is to pass, the plurality of flat refrigerant flow tubes being disposed in parallel and spaced apart from one another in a thickness direction of the plurality of refrigerant flow tubes to form spaces among the plurality of flat refrigerant flow tubes, the thickness direction being perpendicular to the longitudinal direction and the width direction;
• outer fins disposed in a first part of the spaces and joined to the plurality of refrigerant flow tubes;
• at least one cool storage material container containing a cool storage material and disposed in a second part of the spaces other than the first part;
• and
• an inner fin disposed within the cool storage material container and having crest portions extending along the longitudinal direction, trough portions extending along the longitudinal direction, and connection portions connecting the crest portions and the trough portions.