|I'm assuming you HAVE NOT dropped the external drive. |
The USB port you plug the USB cable for the external drive into must be able to supply 500ma of current.
You may need to plug it into a different USB port on the computer.
It's well known that when you use an external USB hub, not all USB devices will work properly when plugged into it.
The external hard drive MAY work with it / be detected fine if it is the ONLY thing plugged into it.
If you're using a USB cable that did not come with the external hard drive, it may be inadequate and not work properly with it.
The drive will not show up in Disk Management and Device Manager if it isn't getting enough current, or if there is some other problem causing it to be not detected such as you have it plugged into an external hub that more than one device is plugged into.
If you DID NOT click on the Safely Remove Hardware icon and choose to STOP accessing the drive while Windows was running, you may have damaged data on the drive when you unplugged it while Windows was running.
That can usually be fixed by using software that can repair the data damage.
Troubleshooting USB device problems including for flash drives, external drives, memory cards.
See Response 1: