Chapter 4 Transient Heat Conduction 4-108 A hot dog is to be cooked by dropping it into boiling water. The time of cooking is to be determined. Assumptions 1 Heat conduction in the hot dog is two-dimensional, and thus the temperature varies in both the axial x- and the radial r- directions. 2 The thermal properties of the hot dog 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 hot dog are given to be k = 0.76 W/m. ° C, ρ = 980 kg/m 3 , C p = 3.9 kJ/kg. ° C, and α = 2 × 10-7 m 2 /s. Analysis This hot dog can physically be formed by the intersection of an infinite plane wall of thickness 2 L = 12 cm, and a long cylinder of radius r o = D /2 = 1 cm. The Biot numbers and corresponding constants are first determined to be 37 . 47 ) C W/m. 76
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