Thermodynamics HW Solutions 350

Thermodynamics HW Solutions 350 - Chapter 4 Transient Heat...

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Chapter 4 Transient Heat Conduction 4-75 A semi-infinite aluminum cylinder is cooled by water. The temperature at the center of the cylinder 10 cm from the end surface is to be determined. Assumptions 1 Heat conduction in the semi-infinite cylinder is two-dimensional, and thus the temperature varies in both the axial x - and the radial r - directions. 2 The thermal properties of the cylinder are constant. 3 The heat transfer coefficient is constant and uniform over the entire surface. 4 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 aluminum are given to be k = 237 W/m. ° C and α = 9.71 × 10 -5 m 2 /s. Analysis This semi-infinite cylinder can physically be formed by the intersection of a long cylinder of radius r o = D /2 = 7.5 cm and a semi-infinite medium. The dimensionless temperature 5 cm from the surface of a semi-infinite medium is first determined from 8951 . 0 1049 . 0 1 ) , ( 1049 . 0 ) 7308 . 0 )( 0468 . 1 (
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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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