I am going to study abroad in Germany, my current location is Malaysia. I am bringing my personal desktop computer (without monitor) as carry-on luggage. The computer chassis size is like this.
Are there any rules or regulations I need to follow?
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It is perfectly okay to do so. I did it before. (To the neighbourning country Netherlands, which has the same rules for immigration). A few tips:
Take enough time to go through security. Electronics are difficult to x-ray and a desktop's size doesn't make it any easier.
If your computer contains a HDD (instead of or along with an SSD), you may want to take that out to protect it from getting damaged. They are very delicate and do not handle movement very well. It wouldn't be the first time someone decides to move your bag and drops it. The rest of the parts handle that fairly well, but wrapping them is still not a bad idea, especially big parts like high end GPUs.
Your computer (parts) will most likely have to be x-rayed thoroughly. You will make everything a lot easier if you take your computer apart as much as possible. Take the motherboard out of the case etc. If this is not possible, don't worry too much, it will simply take a little longer.
Keep all your computer parts (except maybe the HDD) in the same bag. This allows everything to be taken out easier and you won't have to open up all your bags on inspection.