And how do you suppose the air gets out?
More air blowing into the opening than air extraction!
Only pressure difference will cause airflow. See to it that you create a low pressure air zone in aereas that you want air to flow out. Like airdams and/or louvres, or plain low pressure zones, where the flow curves towards the fuselage.

Now, if you place an airdam halfway that huge cut-out, some serious things will happen. Like it is now, your cooling looks good, but does not work as intended.