Chapter 4 Transient Heat Conduction4-81A 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. Assumptions1Heat conduction in the cubic block is three-dimensional, and thus the temperature varies in all x-, y, and z- directions. 2Heat conduction in the cylindrical block is two-dimensional, and thus the temperature varies in both axial x- and radial r-directions. 3The thermal properties of the granite are constant. 4The 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). PropertiesThe thermal properties of the granite are given to be k = 2.5 W/m.°C and α= 1.15×10-6m2/s. Analysis:Cubic block:This cubic block can physically be formed by the intersection of three infinite plane walls of thickness 2L= 5 cm. After 10 minutes: The Biot number, the corresponding constants, and the Fourier number are 400.0)CW/m.5.2()m025.0)(C.W/m40(2=°°==khLBi⎯→⎯==λ110593210580..and Aτα==××=>−tL26115 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.