Thermodynamics HW Solutions 200

Thermodynamics HW Solutions 200 - Chapter 15 Steady Heat...

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Unformatted text preview: Chapter 15 Steady Heat Conduction 3-67 A spherical container filled with iced water is subjected to convection and radiation heat transfer at its outer surface. The rate of heat transfer and the amount of ice that melts per day are to be determined. Assumptions 1 Heat transfer is steady since the specified thermal conditions at the boundaries do not change with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the midpoint. 3 Thermal conductivity is constant. Properties The thermal conductivity of steel is given to be k = 15 W/m ⋅ °C. The heat of fusion of water at 1 atm is h . The outer surface of the tank is black and thus its emissivity is ε = 1. if = 333 7 . kJ / kg Analysis ( a ) The inner and the outer surface areas of sphere are 2 2 2 2 2 2 m 49 . 79 m) 03 . 5 ( m 54 . 78 m) 5 ( = = = = = = π π π π o o i i D A D A We assume the outer surface temperature T 2 to be 5°C after comparing convection heat transfer coefficients at the inner and the outer surfaces of the tank. With this assumption, the radiation heat transfer coefficient at the inner and the outer surfaces of the tank....
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