Why is my iMac is shutting down unexpectadly after few hours of usage?

Hello there, netapier.

It sounds like your iMac is powering down unexpectedly. When that occurs, it may be an indicator that you should reset your System Management Controller. How to do this is outlined in the following Knowledge Base article:

Resetting the System Management Controller (SMC) on your Mac - Apple Support

On Mac Pro, iMac, Mac mini, and Xserve

To reset the SMC on Intel-based Mac Pro, iMac, and Mac mini computers, as well as Xserve:

1. Shut down the computer.
2. Unplug the power cord.
3. Wait fifteen seconds.
4. Attach the power cord.
5. Wait five seconds, then press the power button to turn on the computer.

For Intel-based Xserve computers that are not responding, you can shut down locally or by using remote commands. You can also shut down by pressing and holding the power button for five seconds.

Learn more

The SMC is responsible for many low-level functions on Intel-based Macs. These functions include:

• Responding to presses of the power button
• Responding to the display lid opening and closing on portable Macs
• Battery management
• Thermal management
• The SMS (Sudden Motion Sensor)
• Ambient light sensing
• Keyboard backlighting
• Status Indicator Light (SIL) management
• Battery status indicator lights
• Selecting an external (instead of internal) video source for some iMac displays

Resetting the SMC does not reset or otherwise change the contents of PRAM (also known as NVRAM) on Intel-based Macs.

If you continue to see the issue, the following is a much more in-depth article on troubleshooting spontaneous restarts:

OS X: When your computer spontaneously restarts or displays "Your computer restarted because of a problem." - Apple Support

Thanks for reaching out to Apple Support Communities.

Cheers.