When the transportation of natural gas in a pipeline is not feasible for economic or other reasons, it is first liquefied at about −160°C, and then transported in specially insulated tanks placed in marine ships. Consider a 4-m·diameter spherical tank that is filled with liquefied natural gas (LNG) at −160°C. The tank is exposed to ambient air at 24°C with a heat transfer coefficient of 22 W/m2·K. The tank is thinshelled and its temperature can be taken to be the same as the LNG temperature. The tank is insulated with 5-cm-thick super insulation that has an effective thermal conductivity of 0.00008 W/m·K. Taking the density and the specific heat of LNG to be 425 kg/m3 and 3.475 kJ/kg·°C, respectively, estimate how long it will take for the LNG temperature to rise to −150°C.
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