At the ASHRAE winter conference 2018, we proposed liquid immersion system that utilizes the natural convection of refrigerant as a cooling method for high performance computing (HPC) systems with a PUE of 1.04. The system eliminated the pumps and fans required for circulating refrigerant in a liquid tub. In a natural convection system, convection is quite sensitive to the geometry of the environment. To demonstrate effective cooling, we need to carefully design the geometry of the liquid tub by comparing it with the conventional forced convection system. In this paper, design guidelines were verified in detail from the viewpoint of realistic operation. As a result, a design guideline for a highly efficient cooling system with a PUE of below 1.02 was established when 35 degrees C cooling water was flowed into the cold plates. We also examined the impact of slot insertion/removal and CPU task fluctuations on the entire cooling efficiency, which are of the greatest concern in actual system operation. Our results showed that slot insertion and removal and task fluctuation had little influence on other slots or the CPU cooling efficiency. There was also almost no constraint on the operation of the entire system with respect task allocation. These results indicate that the system with natural convection exhibits promising potential for practical high-efficient cooling technology for high-heat density computer systems.