Thermodynamics HW Solutions 358

Thermodynamics HW Solutions 358 - Chapter 4 Transient Heat...

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Chapter 4 Transient Heat Conduction 4-80 A cylindrical ice block is placed on a table. The initial temperature of the ice block to avoid melting for 2 h is to be determined. Assumptions 1 Heat conduction in the ice block is two-dimensional, and thus the temperature varies in both x - and r - directions. 2 Heat transfer from the base of the ice block to the table is negligible. 3 The thermal properties of the ice block are constant. 4 The heat transfer coefficient is constant and uniform over the entire surface. 5 The Fourier number is τ > 0.2 so that the one-term approximate solutions (or the transient temperature charts) are applicable (this assumption will be verified). Air T = 20 ° C x r ( r o , L ) Insulation Ice block T i Properties The thermal properties of the ice are given to be k = 2.22 W/m. ° C and α = 0.124 × 10 -7 m 2 /s. Analysis This cylindrical ice block can be treated as a short cylinder that can physically be formed by the intersection of a long cylinder of diameter D = 2
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