In this study, to apply hydrogen energy to ship engine and to generate effective hydrogen production, we investigated the effects of high temperature $H_2SO_4$ feed rate and cooling water rate to pump parts with fixed frequency needed to reciprocate motion and a simulation was conducted at each condition. In the fixed frequency and cooling water inlet flow rate of 0.5 Hz and 3.9 kg/s, we changed the high temperature $H_2SO_4$ flow rate to 47.46 kg/s (it is 105 % of 45.2 kg/s), 49.72 kg/s (110 %), and 51.98 kg/s (115 %). Also, at 0.5 Hz and 45.2 kg/s of frequency and high temperature $H_2SO_4$ flow, the thermal hydraulic analysis was performed at the condition of 95 % (3.705 kg/s), 90 % (3.51 kg/s), and 85 % (3.315 kg/s). In overall simulation cases, the physical properties of materials are more influential to the temperature increase in the pump part rather than the changes on the feed rate of high temperature $H_2SO_4$ and cooling water. A continuous operation of pump was also capable even if the excess feed of high temperature $H_2SO_4$ of about 15 % or the less feed of cooling water of about 15 % were performed, respectively. When the increasing feed of high temperature $H_2SO_4$ of up to 5 %, 10 %, and 15 % were compared with base flow (45.2 kg/s), the deviation of time period rose to a certain temperature and ranged from 0 to 4.5 s in the same position (same material). In case of cooling water, the deviation of time period rose to a certain temperature and ranged from 0 to 5.9 s according to the decreasing feed changes of cooling water at 5 %, 10 %, and 15 % compared to a base flow (3.9 kg/s). Finally, the additional researches related to the two different materials (Teflon and STS for Pitch and End-plate), which are concerned about the effects of temperature changes to the parts contacting different materials, are needed, and we have a plan to conduct a follow-up study.