The NZXT H440 case has developed a reputation for not being the best at airflow and cooling. I had my suspicions so I put it to the test with both Corsair SP120 and Noctua NF-F12 fans cooling my H105. I tested both options for a pull configuration (pulling air out of the case or pulling air in) and checked temperatures with the top of the case on and with it removed. The results are pretty telling in regards to just how much the H440 restricts airflow under heavy loads.
The ambient room temperature for all tests was steady at 70 degrees Fahrenheit.