Thermodynamics HW Solutions 289

# Thermodynamics HW Solutions 289 - m 92 12 m 6 m 4 1 08 1 ln...

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Chapter 3 Steady Heat Conduction 3-177 A cylindrical tank containing liquefied natural gas (LNG) is placed at the center of a square solid bar. The rate of heat transfer to the tank and the LNG temperature at the end of a one-month period are to be determined. Assumptions 1 Steady operating conditions exist. 2 Heat transfer is two-dimensional (no change in the axial direction). 3 Thermal conductivity of the bar is constant. 4 The tank surface is at the same temperature as the iced water. Properties The thermal conductivity of the bar is given to be k = 0.0006 W/m °C. The density and the specific heat of LNG are given to be 425 kg/m 3 and 3.475 kJ/kg °C, respectively, -160 ° C L = 1.9 m D = 0.6 m 20 ° C 1.4 m Analysis The shape factor for this configuration is given in Table 3-5 to be
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Unformatted text preview: m 92 . 12 m 6 . m 4 . 1 08 . 1 ln ) m 9 . 1 ( 2 08 . 1 ln 2 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π = D w L S Then the steady rate of heat transfer to the tank becomes [ ] W 1.395 = ° − − ° = − = C ) 160 ( 20 ) C W/m. 0006 . )( m 92 . 12 ( ) ( 2 1 T T Sk Q & The mass of LNG is kg 07 . 48 6 m) 6 . ( ) kg/m 425 ( 6 3 3 3 = π = ρπ = ρ = D V m The amount heat transfer to the tank for a one-month period is J 840 , 615 , 3 s) 3600 24 W)(30 395 . 1 ( = × × = Δ = t Q Q & Then the temperature of LNG at the end of the month becomes [ ] C-138.4 ° = ° − − ° = − = 2 2 2 1 C ) 160 ( ) C J/kg. kg)(3475 (48.07 J 840 , 615 , 3 ) ( T T T T mC Q p 3-178 ··· 3-184 Design and Essay Problems KJ 3-132...
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