The issue may be the formatting of the drive, Windows has difficulty with what the iMac [or any Mac] uses. If Windows Disk Management can't see the drive it can't assign a drive letter and without that File Explorer can't see the drive. Some External drives can be found that are compatible with both Windows and Mac but it'll be on the packaging or advertisement. I use a Linux Mint machine to check drives, salvage data, clean and format or reformat to a different type. The included program GPARTED can work with many formats and is also available as a LiveCD .iso file to create a bootable disc.
Almost forgot, some versions of the Mac OS can read NTFS-formatted drives but need additional software for doing more than that, never found a good one before my MacBook Pro died.