Thermodynamics HW Solutions 41

Thermodynamics HW Solutions 41 - Chapter 1 Basics of Heat...

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Chapter 1 Basics of Heat Transfer 1-84 A styrofoam ice chest is initially filled with 40 kg of ice at 0 ° C. The time it takes for the ice in the chest to melt completely is to be determined. Assumptions 1 Steady operating conditions exist. 2 The inner and outer surface temperatures of the ice chest remain constant at 0 ° C and 8 ° C, respectively, at all times. 3 Thermal properties of the chest are constant. 4 Heat transfer from the base of the ice chest is negligible. Properties The thermal conductivity of the styrofoam is given to be k = 0.033 W/m ⋅° C. The heat of fusion of ice at 0 ° C is 333.7 kJ/kg. Analysis Disregarding any heat loss through the bottom of the ice chest and using the average thicknesses, the total heat transfer area becomes A =− + ×− = = () ()() . 40 3 40 3 4 40 3 30 3 5365 05365 cm m 22 The rate of heat transfer to the ice chest becomes & (. ) . . Qk A T L == ° ° = Δ 0 033 05365 003 472 W/m. C) m (8 0) C m W 2 The total amount of heat needed to melt the ice completely is Qm h if = (, 40 13 348 kg)(333.7 kJ / kg) kJ
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