Inspiron shuts off by itself after a few minutes of running

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This is normal on a lot of newer comnputers

Your fan speeds up and slows down in response to temperature inside the computer. More so the CPU.

In the case of too much heat it may also shut down

I would suggest getting a can of compressed air made for computers

take it outside, take of any panels you can (keep all the screws ina container) and blow all the gunk out of there,

Really go to town around the fan (you might want to wear eye protection)

DONT poke the nozzle into anything

While you are in there just check that the cpu cooler itself is not loose if you can get to it

If it is it will have to be re-seated.

If it needs re-seating don't just take it off and put it back on as that might make things worse with your temperature problem

They have to be cleaned and new thermal grease put on

use a lptop coling pad with at least three fans and dont use a laptop on soft surfaces as this attracts more dirt and blocks the cooling vents.

If the Computer is turning off randomly without any error message then the issue may be with the power supply unit.