My computer shuts down automatically without any alert

It is possible, that your system is getting over heated because of dust accumulation. It is also possible that some virus has got spread which your antivirus is not able to detect.
One option right now, is installing CC Cleaner in your system which keep cleaning your system from unnecessary internet files, temporary ones and other cookies.
If that too doesn't work, you might have to go for internal cleaning or a factory reset, but make sure you take a full backup of your system before you do anything.

Try running your computer in safe mode. If you are not facing any problem in safe mode, I am sure your computer is infected.

Starting computer in safe mode:
To start you computer in safe mode press F8 button while booting. You should press F8 before the Windows logo appear. If the Windows logo appears then 'restart' your system and try the same. If you want to use internet then choose 'Safe mode with networking'. In safe mode only Microsoft drivers and software will be started.

Once you press F8, advanced booting option screen appears. It is a black and white screen.

Computer still facing restart issue in Safe Mode:
If you are again facing the same problem then the problem is related to hardware. It might be problem with SMPS or motherboard. In that case call technician.

I don't think it will be an virus infection, because you have mentioned about the "Date and Time" on your computer was changing every time when you restarts your PC.

Probelm:
1.Computer Shutdown automatically after working around 30 minutes without any alerts.
2. Computer's Date and Time automatically changes back to it's initial time (Probably the built in date).

Possible causes:
As the computer runs about 30 minutes we can avoid the possiblity of "Jam of CPU Button".
1. Your CMOS battery may be old.
2. Your CPU is not clean or have dust.
Ithink it will be an hardware problem so, please do consider the following solutions.

Solutions:
I have a strong feeling that it might because of BIOS issue. As the date and time changes in your computer, the replacement of CMOS Battery (which associated with the storing of Date and time when computer is turned off) will be the solution.

1. As the first step just open the CPU case and look whether the CPU is full of dust. Remove the dust with small brush and you can also clean the RAM and reinsert it.
2. If the above problem still exist, then please do buy a "CMOS Battery" and replace your old one. It must solve your problem. Cost of a CMOS Battery is around 20-30Rs/-. I will attach the image of a CMOS Battery.

How to Replace CMOS Battery:
Open the CPU case and give a little push on the CMOS Battery. It will come up and you can remove it and insert the new battery with a simple push.

Note: If you can please reply me with the Date and Time which your computer resets after every shutdown and check whether this Date and Time is similar after every restart. Please do the above solutions and write your results whether it worked or not. We will always happy to help.