Thermodynamics HW Solutions 359

Thermodynamics HW Solutions 359 - Chapter 4 Transient Heat...

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Chapter 4 Transient Heat Conduction 4-81 A cubic block and a cylindrical block are exposed to hot gases on all of their surfaces. The center temperatures of each geometry in 10, 20, and 60 min are to be determined. Assumptions 1 Heat conduction in the cubic block is three-dimensional, and thus the temperature varies in all x -, y , and z - directions. 2 Heat conduction in the cylindrical block is two-dimensional, and thus the temperature varies in both axial x - and radial r- directions. 3 The thermal properties of the granite 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). Properties The thermal properties of the granite are given to be k = 2.5 W/m. ° C and α = 1.15 × 10 -6 m 2 /s. Analysis : Cubic block: This cubic block can physically be formed by the intersection of three infinite plane walls of thickness 2 L = 5 cm. After 10 minutes : The Biot number, the corresponding constants, and the Fourier number are 400 . 0 ) C W/m. 5 . 2 ( ) m 025 . 0 )( C . W/m 40 ( 2 = ° ° = = k hL Bi ⎯→ ⎯= = λ 11 05932 10580 .. and A τ α == ×× => t L 2 6 115 10
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This note was uploaded on 01/19/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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