tuckerlm
That is a definite improvement although the inefficiency of EDFs (about half that of a prop) does not make them ideal for load carrying applications. The size of battery needed tends to be the load.
You are correct about the using a reducing "nozzle" of about 85% of the Fan Swept Area (FSA). Note this is the area of the fan and does not include the area of the fan hub/motor. Such a nozzle optimises the exhaust velocity but if your plane is a slower flyer there can be advantage in leaving the exhaust at the FSA to gain maximum static thrust. Optimising EDF ducting does require a bit of mathematics!
A rather stylized EDF in a duct with a thrust tube reducing to 85% FSA.
With an inlet duct the EDF itself does not use a bell mouth. However for maximum static thrust the actual inlet mouth should be radiused to maximise inlet flow.
It is worth noting that the most efficient EDF has the very minimum of ducting which is exactly why modern airliners stick their turbo fans on the "outside" rather than buried within the structure, however
supersonic jets do not do this as the shock waves from such an externally mounted arrangement would be structurally dangerous.
I hope this helps.