Is there any limitation with Arduino Nano serial communication distance?
For that sort of difference you are better using RS-485 instead of UART.  UART is really only designed for short-distance communication.  

Converting UART to RS-232 will give an improvement, but switching to RS-485 instead will give you the ability to create a multi-drop bus for connecting more than two Arduinos together over a long distance.


UART uses 5V logic level signalling (on the normal Arduinos - 3.3V on most 32-bit boards). It has a "weak drive" and is highly susceptible to induced noise over longer distances.
RS-232 uses ±10V "Non Return to Zero" signalling. This gives far greater immunity to noise and a stronger drive for greater distances.
RS-485 (and the associated peer-to-peer RS-422) use differential signalling. This gives the greatest immunity to noise over the longest distances. 


In summary:


RS-232 can be used if you only want to connect two devices together in a low noise environment. 
RS-422 can be used to connect two devices together in a high noise (industrial) environment. 
RS-485 can be used to connect lots of devices together in a high noise environment.


For more information on how they work there are some good Wikipedia pages:


RS-232
RS-422
RS-485


For interfacing any of these to an Arduino you will need extra hardware ("Driver Chips"). For example:


RS-232: MAX232
RS-422: MAX1184
RS-485: MAX485




There is also "CAN", which is a more modern replacement for RS-485 and is used in many industrial and automotive environments. As this is a newer technology than RS-485 there are fewer resources available and "initial cost to entry" can be higher.