A 0.6-m-diameter, 1.9-m-long cylindrical tank containing liquefied natural gas (LNG) at 2160°C is placed at the center of a 1.9-m-long 1.4-m × 1.4-m square solid bar made of an insulating material with k = 0.0002 W/m · K. If the outer surface temperature of the bar is 12°C, determine the rate of heat transfer to the tank. Also, determine the LNG temperature after one month. Take the density and the specific heat of LNG to be 425 kg/m3 and 3.475 kJ/kg·°C, respectively.

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Air, -5°C h = 20 W/m².K T₁ = 120°C D = 127 mm T₂: W Concrete bar k = 1.7 W/m-K