I accidentally happened to install windows 8 (64 bit) in my 32 bit machine.
How do you know? How do you know that the copy you installed was 64-bit and that the system was 32-bit?
Are there any problem that can occur in future?
Yes, lack of ability to boot or execute any of the 64-bit files. For all intents and purposes, it is essentially impossible to execute a 64-bit instruction on 32-bit hardware, and while 64-bit Windows may have some 32-bit files, the main parts are 64-bit, so it won’t even boot.
It is running quite smoothly right now.
Then one of two things is almost certainly happening:
- The hardware is in fact 64-bit (as others have mentioned, since a 64-bit system can run a 32-bit OS, it may have been 32-on-64, leading to a misconception of the hardware)
- The installation media was 32-bit (it could have been a “hybrid” source containing both 32-bit and 64-bit Windows and so it automatically detected the 32-bit hardware and installed that)
In either case, if it is working at all, then you are good and should not have any problems because an architecture-mismatch would be immediately noticeable since it won’t boot, let alone give errors about the executable files being an “invalid Windows file”.