A spherical vessel with thin walls has a diameter D = 4 m, and is used to store liquefied natural gas (LNG), so its temperature under normal operating conditions is, Ti = 112 K. A larger thin-walled spherical container of diameter D. = 4.2 m surrounds the LNG vessel, and both are concentric about a common centre, so that the intervening cavity is uniform in thickness, and filled with atmospheric helium (k = 0.1151 W/m K). The air surrounding the outer sphere is normally at T = 300 K. What is the mass rate in kg/s at which gaseous methane vents from the system? Use 5.1 x 10 J/kg as methane's latent heat of vaporization, and for air you may use p = 1.7458 kg/m, cp = 1007 J/kgK, = 132.5 x 10-7 kg/sm, k = 0.0181 W/mK, a = 1.03 x 10-7 m/s, and Pr = 0.737. You can estimate the natural-convection heat-transfer coefficient for the sphere from Nup = 2 + 1/4 0.589 Rap Pr 0.7 [1+ (0.469/Pr) 9/164/9Rap 1011 Rayleigh number for the relevant characteristic length x is Rax= 8B(T-T)x For a sphere, thermal resistance Re, cand = R 47k (15 marks)