Prior to docking for the inspection cargo tanks of LNG carrier should be warmed up to the normal temperature. This operations are performed by supplying the hot vapor heated by the steam heaters and transferred by the gas compressors installed on board ship to the cargo tank bottom through the closed loop piping for the safety against an explosive gas of LNG. Before starting the warming up, small amount of LNG residue is left at the bottom of tanks, therefore hot vapor is supplied to the bottom to expedite the vaporization of LNG residue at an early stage of operation. Mixture of hot and vaporized gas rises up toward the tank top transferring the heat to the cold vapor and tank wall according to the thermal transfer rule. In order to maintain the maximum tank pressure under a certain level in closed loop system, increment of vapor volume with temperature and time should be discharged to the atmosphere through the control valve by sensing the tank pressure according to the gas rule. In this paper equations of thermal equilibrium and mass balance are established for each part of tank and vapor divided vertically into three portions and solved as the initial value problem by means of Picard method.In this analyses author introduced two kinds of thermal efficiency, mixing efficiency of hot and cold vapor η and enthalpy contribution efficiency ε. On the other hand surface heat transfer coefficient at the tank wall and liquid surface being an important factor for the evaluation of heat transfer from hot vapor, Merk prins' equation of natural convection for tank wall and Colburn's equation of forced convection of turbulent flow for the surface of LNG residue were used respectively.
