Chapter 4 Transient Heat Conduction4-75A 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. Assumptions1Heat conduction in the semi-infinite cylinder is two-dimensional, and thus the temperature varies in both the axial x- and the radial r- directions. 2The thermal properties of the cylinder are constant. 3The 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). PropertiesThe thermal properties of aluminum are given to be k = 237 W/m.°C and α= 9.71×10-5m2/s. Analysis This semi-infinite cylinder can physically be formed by the intersection of a long cylinder of radius ro= 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 8951.01049.01),(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.