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# HW5 - PROBLEM 5.13 KNOWN Heat transfer from a rod is to be...

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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. h = 150. ± 7.00% W/m 2 -K (95%) D = 200. ± 0.500 mm (95% assumed) k = 0.600 ± 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 2 2 2 Nu h D k Nu Nu Nu u u u u h D k Ρ Τ Λ Ξ Λ Ξ Λ Ξ = ± + + ΢ Υ Μ Ο Μ Ο Μ Ο Ν Π Ν Π Ν Π ΢ Υ Σ Φ = 1/ 2 2 2 2 Nu h D k 2 D h hD u u u u k k k Ρ Τ Λ Ξ Λ Ξ Λ Ξ = ± + + ΢ Υ Μ Ο Μ Ο Μ Ο Ν Π Ν Π Ν Π ΢ Υ Σ Φ = where u h = (0.0700)(150.) = 10.5 W/m 2 -K u D = 0.000500 m u k = (0.0200)(0.600) = 0.0120 W/m-K Then, we estimate the Nusselt number here to be Nu = hD/k ± u Nu = 5.00 ± 0.385 (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

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HW5 - PROBLEM 5.13 KNOWN Heat transfer from a rod is to be...

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