This equation demonstrates the usage of F12, but it represents a non-physical case since it would be impossible to position two finite objects such that they can see only a portion of each other and "nothing" else. On the contrary, the complementary view factor (1 - F12) cannot be neglected as radiation energy sent in those directions must be accounted for in the thermal bottom line.
A more realistic problem would consider the same two objects surrounded by a third surface that can absorb and readmit thermal radiation yet is non-conducting. In this manner, all thermal energy that is absorbed by this third surface will be readmitted; no energy can be removed from the system through this surface. The equation describing the heat flow from Object 1 to Object 2 for this arrangement is,