Should I consider the heat tranfer of the rod to air and water separately for the two dimensional heat flow?
FOR THIS 2D TRANSIENT, YES.
How to determine the Biot Number?Should I consider two Biot Numbers, one is for air and the other one is for water?
I WOULD CONSIDER HEAT TRANS COEF FOR BOTH AIR AND WATER.
THIS CAN BE MESSY- ESPECIALLY WITH NATURAL CONVECTION AND RADIATION FOR THE AIR SURFACE.