It's easy to fix that a Western Digital external hard drive does not show up in Finder on your MacBook. However, according to your description, it seems like your Western Digital external hard drive is dead, but you can still do some troubleshooting before you send it to repair or change to a new one.
Method 1: Check it in Disk Utility. Check whether you can see your drive in Disk Utility. If it shows in Disk Utility, try to mount and unmount again. If not working, run First Aid to check and repair the logical error on your drive.
Method 2: Run Terminal. You can run Terminal to check your drive. Type in diskutil list to list all the drives and partitions that have been hidden in Disk Utility.
If your drive still does not show in Terminal, chances are your hard drive has died. You can send your drive to a local professional to repair or replace it with a new one.