Answer the following, A cylindrical pure aluminum tube has LN2 flowing through i

Question

Answer the following,

A cylindrical pure aluminum tube has LN2 flowing through it. It enters the tube at 77K as saturated liquid . The outer surface is exposed to air at 25 degree C with a heat transfer coefficient of 35 W/m2K. The inner surface heat transfer coefficient is 120 W/m K The inner diameter is 2 cm and the tubing is 0.2cm thick. If the tube is 5 meters long and the mass flow rate is 0.2kg's, will the LN2 coming out of the tube be 100% vapor? The heat of vapourisation for LN2 is 125kJ/kg.

Explanation / Answer

Let saturated temperature of fluid be T=77 K

Outer surface temperature Ta=25+273=298 K

Conductivity k of aluminium=210 W/mK

Thermal Resistance at inner convective boundary=1/h1A1=1/(120*2*pi*2/100*5)=0.013263

Thermal Resistance of cylinder=ln(r2/r1)/(2*pi*k*L)=ln(2.2/2)/(2*pi*210*5)=0.000014

Thermal Resistance at outer convective boundary=1/h2A2=1/(35*2*pi*2.2/100*5)=0.041338

Heat flow per unit time Q=(T-Ta)/(1/h1A1+ln(r2/r1)/(2*pi*k*L)+1/h2A2)

=(298-77)/(0.013263+0.000014+0.041338)=4046.50 W

Heat flux required to form vapour q=m*l=0.2*125*1000W=25000W

Since heat flux reuired>Heat flow calculated=4046.5W,

No. LN2 would not end up as 100% vapour at the end.

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