If the system is a single-phase liquid in a closed loop, then increasing the pipe size from 2 inches to 4 inches will decrease the velocity by a factor of 4 and reduce the film coefficient on the inside by a factor of about 3.  The area will double but the change in the heat transfer rate will be dependent upon the fractional resistance offered by the material inside the pipe.  If the overall heat transfer rate is dominated by the outside film coefficient, then the heat transfer rate may increase nearly proportional to the area increase.  If the overall heat transfer rate is dominated by the inside coefficient, then the heat transfer rate may decrease by nearly 35%.  It is important to be able to discern the distribution of heat transfer resistances among the inside, outside and wall conduction components in order to determine if the change in pipe size will have the desired effect.