A liquefied natural gas(LNG) in cryogenic liquid is converted back into gaseous form for distribution to residential and industrial consumers. In this re-gasification process, LNG supplies a plenty of cold thermal energy about $83.7{ imes}10^4kJ/kg$. The LNG cold thermal energy is utilized for the re-liquefaction process of cryogenic fluids such as Nitrogen, Hydrogen and Helium, and ice manufacturing process and air-conditioning system in some advanced countries. Therefore, it is also necessary to establish the recovery systems of the LNG cold thermal energy around Incheon, Pyungtaek and Tongyung LNG import terminals in our country. Methane is used as working fluid in this paper, which is the major component of LNG over 85 % by volume, in order to investigate the flow behavior characteristics of LNG with phase change at low heat flux. This paper presents the effects of pipe diameters, pipe inclinations and saturation pressures on the flow boundaries of methane flowing in a cryogenic heat exchanger tube, together with those of nitrogen, propane, R11 and R134a. The outcomes obtained from this theoretical researches are also compared with previous experimental data. It was also found that the effect of pipe inclination on the methane flow boundaries was significant.