HW-5_solutions

# HW-5_solutions - PROBLEM 5.13 KNOWN Heat transfer from a...

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PROBLEM 5.13 KNOWN: Heat transfer from a rod is to be determined. Nu = hD/k is the nondimensional heat transfer. u h = 150 ± 7% W/m 2 -K (95%) u d = 20 ± 0.5 mm (95% assumed) u k = 0.6 ± 2% W/m-K (95% assumed) FIND: u Nu SOLUTION At the known level of uncertainty provided: Nu = f(h,D,k) then, 1/2 222 Nu h D k Nu Nu Nu uu u u hDk ⎡⎤ ∂∂∂ ⎛⎞ + + ⎢⎥ ⎜⎟ ∂∂ ⎝⎠ ⎣⎦ = 22 2 Nu h D k 2 Dh h D u u kk k + + = 2 Nu 2 0.02 150 150x0.02 u 10.5 0.005 0.012 0.4 0.6 0.6 0.6 + + where u h = (0.07)(150) = 10.5 W/m 2 -K u D = 0.0005 m u k = (0.02)(0.6) = 0.012 W/m-K Then, we estimate the Nusselt number here to be Nu = hD/k ± u Nu = 5 ± 0.4 (95%) So, Nusselt number can be determined within about 8% in this range of values. COMMENT The level of uncertainty analysis (design-stage, advanced design-stage, …) in the result depends on the level of uncertainty values given or available. This problem solution provides the propagation of uncertainty from the variables to the result.

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PROBLEM 5.14 KNOWN: R = 30 P = 500 W Ohmmeter Resolution: 1
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HW-5_solutions - PROBLEM 5.13 KNOWN Heat transfer from a...

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