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Thermodynamics HW Solutions 309

# Thermodynamics HW Solutions 309 - Chapter 4 Transient Heat...

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Chapter 4 Transient Heat Conduction 4-36 Large brass plates are heated in an oven. The surface temperature of the plates leaving the oven is to be determined. Assumptions 1 Heat conduction in the plate is one-dimensional since the plate is large relative to its thickness and there is thermal symmetry about the center plane. 3 The thermal properties of the plate 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 properties of brass at room temperature are given to be k = 110 W/m. ° C, α = 33.9 × 10 -6 m 2 /s Analysis The Biot number for this process is Bi hL k == ° ° = (80 )( . ) () . W/m . C m W/m. C 2 0015 110 0 0109 The constants λ 1 and A 1 corresponding to this Biot number are, from Table 4-1, 11 01039 10018 .. and A The Fourier number is τ α ×× => t L 2 6 339 10 10 90 4 0 2 (. m / s)( min 60 s / min) m) 2 2 Plates 25 ° C Furnace, 700 ° C Therefore, the one-term approximate solution (or the transient temperature charts) is applicable. Then the
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