You cannot recover a data file or a database in
NOARCHIVELOG mode, since there's no redo entries that you could apply to your previous backups to roll the data files forward up to the point of failure.
If the database is in
ARCHIVELOG mode, the ARCn process constantly copies online redo log files to a persistent area when they are full, so that you can later apply the redo entries to the previous backups. Copied online redo log files are called archive log files.
NOARCHIVELOG mode, LGWR writes redo entries to redo log files while DBWR writes data blocks to data files, however redo log files full of redo entries are not copied, but are overwritten in a round-robin fashion, and thus no redo data is available to apply to the previous backups.
Therefore, if your database is in
NOARCHIVELOG mode, you cannot recover your database up to the point of failure, you can only restore it to a previous state which is the time of one of your backups.
For more info, read the section "Choosing Between NOARCHIVELOG and ARCHIVELOG Mode" in Database Administrator's Guide.