If your external hard disk is not detecting then there may be many reasons. Reasons may be hard disk's partition issue or dead USB port in your computer or driver problem in your windows.
1) First see that, is your hard disk showing in Disk management? For that first press "Windows +R" in your computer. It will open RUN box. Type there "diskmgmt.msc" without inverted commas and press Enter. In disk management your external hard disk should show up. If it is not showing up, then you can be sure there is some problem with hard disk or port.
2) Check your USB port in computer. Unplug your hard disk and plug it to another USB port. If your hard disk is showing then the previous port is dead. If you are connecting to USB hub, then try to plug that hub to another computer. Because some USB hubs don't get enough power to function hard disk. If all is OK and still your hard disk is not detecting then there may be driver issue.
3) To check the driver, you have to open Device Manager. For that first press "Windows +R" in your computer. It will open RUN box. Type there "devmgmt.msc" without inverted commas and press Enter. Look at Disk drives and see that is there any devices with a yellow exclamation mark next to it. If there is yellow exclamation mark, then make sure there is a driver problem. Press Right-click of the mouse at the device with a yellow exclamation mark. Select Properties and see the error message. This will help you solve the problem. If you want to fix the problem with your own then do a Google search for the error message.
If still you are unable to fix the problem then I suggest you to take your hard disk to any professional technician.