Homework Materials - Convection Correlations

Geometry Forced, flat plate Conditions 𝑅𝑒𝐿 < 5 × 105 𝑃𝑟 > 0.6 Correlation ̅̅̅̅̅̅ 𝑁𝑢𝐿 = 0.664 𝑅𝑒𝐿0.5 𝑃𝑟1/3 [none] 𝑇 +𝑇 ̅̅̅̅̅̅ 𝑁𝑢𝐿 = 0.036𝑃𝑟1/3 (𝑅𝑒𝐿0.8 − 23200) 5 × 105 < 𝑅𝑒𝐿 < 108 0.6 < 𝑃𝑟 < 60 Forced, cylinder Notes Zukauskas 𝑃𝑟 0.25 𝑚 𝑛 ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 𝐶 𝑅𝑒𝐷 𝑃𝑟 ( ) 𝑃𝑟𝑠 -Properties at 𝑇𝑓 = 𝑠 ∞ 2 -Laminar flow 𝑇 +𝑇 -Properties at 𝑇𝑓 = 𝑠 ∞ 2 -Mixed correlation -Properties at 𝑇∞ except 𝑃𝑟𝑠 at 𝑇𝑠 - 𝐶, 𝑚 dependent on 𝑅𝑒𝐷 𝑃𝑟 < 10: 𝑛 = 0.37 𝑃𝑟 > 10: 𝑛 = 0.36 Forced, sphere Forced, bundle of tubes Liquid or gas 3.5 < 𝑅𝑒𝐷 < 7.6 × 104 0.7 < 𝑃𝑟 < 380 Whitaker ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 2 + (0.4𝑅𝑒𝐷0.5 -Properties at 𝑇∞ except 𝜇𝑠 at 𝑇𝑠 Liquid metal 3.6 × 104 < 𝑅𝑒𝐷 < 2 × 105 Witte -Properties at 𝑇𝑓 = 1 < 𝑅𝑒𝐷 < 100 0.7 < 𝑃𝑟 < 500 103 < 𝑅𝑒𝐷 < 2 × 105 0.7 < 𝑃𝑟 < 500 𝜇 0.25 + 0.06𝑅𝑒𝐷0.67 )𝑃𝑟 0.4 ( ) 𝜇𝑠 ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 2 + 0.386(𝑅𝑒𝐷 𝑃𝑟)0.5 Zukauskas-in-line tubes 0.25 𝑃𝑟 ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 0.81 𝑅𝑒𝐷0.4 𝑃𝑟 0.36 ( ) 𝑃𝑟𝑠 Zukauskas-staggered tubes 𝑃𝑟 0.25 ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 0.9 𝑅𝑒𝐷0.4 𝑃𝑟 0.36 ( ) 𝑃𝑟𝑠 Zukauskas-in-line tubes 𝑆𝑇 ≥ 0.7: 𝑆𝐿 𝑃𝑟 0.25 ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 0.27 𝑅𝑒𝐷0.63 𝑃𝑟 0.36 ( ) 𝑃𝑟𝑠 Zukauskas-staggered tubes 𝑆𝑇 < 2: 𝑆𝐿 𝑆𝑇 0.2 𝑃𝑟 0.25 ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 0.35 ( ) 𝑅𝑒𝐷0.6 𝑃𝑟 0.36 ( ) 𝑆𝐿 𝑃𝑟𝑠 𝑆𝑇 ≥ 2: 𝑆 𝐿 -Properties at 𝑇̅ = at 𝑇𝑠 -Laminar regime 𝑇𝑠 +𝑇∞ 2 𝑇𝑖𝑛 +𝑇𝑜𝑢𝑡 2 except 𝑃𝑟𝑠 𝑇 +𝑇 -Properties at 𝑇̅ = 𝑖𝑛 2 𝑜𝑢𝑡 except 𝑃𝑟𝑠 at 𝑇𝑠 -Transition regime 𝑆 -𝑆𝑇 < 0.7 is not an effective heat 𝐿 exchanger for in-line tubes ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 0.40 𝑅𝑒𝐷0.6 𝑃𝑟 0.36 ( 𝑅𝑒𝐷 > 2 × 105 0.7 < 𝑃𝑟 < 500 Internal, tubes 𝐿/𝐷 > 0.05 𝑅𝑒𝐷 𝑃𝑟 𝑅𝑒𝐷 < 2300 𝐿/𝐷 < 0.05 𝑅𝑒𝐷 𝑃𝑟 𝑇𝑠 = 𝑐𝑜𝑛𝑠𝑡 𝑃𝑟 > 5 𝑅𝑒𝐷 > 104 0.6 < 𝑃𝑟 < 160 𝐿 ≥ 10 𝐷 𝐺𝑧𝐷−1 = Natural, vertical plate 𝐺𝑟𝐿 𝑃𝑟 = 𝑅𝑎𝐿 < 108 𝑅𝑎𝐿 > 1010 Natural, horizontal plat 105 < 𝑅𝑎𝐿𝑐 < 107 Upper surface hot, lower surface cool 107 < 𝑅𝑎𝐿𝑐 < 1010 Upper surface hot, lower surface cool 105 < 𝑅𝑎𝐿𝑐 < 1010 Lower surface hot, upper surface cool 𝑃𝑟 0.25 ) 𝑃𝑟𝑠 Zukauskas-in-line tubes 0.25 𝑃𝑟 ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 0.021 𝑅𝑒𝐷0.84 𝑃𝑟 0.36 ( ) 𝑃𝑟𝑠 Zukauskas-staggered tubes 𝑃𝑟 > 1: 𝑃𝑟 0.25 0.84 0.36 ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 0.022 𝑅𝑒𝐷 𝑃𝑟 ( ) 𝑃𝑟𝑠 𝑃𝑟 = 0.7: ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 0.019 𝑅𝑒𝐷0.84 𝑞𝑠′′ = 𝑐𝑜𝑛𝑠𝑡.: ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 4.36 𝑇𝑠 = 𝑐𝑜𝑛𝑠𝑡: ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 3.66 Hausen 0.0668𝐺𝑧𝐷 ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 3.66 + 2/3 1 + 0.04 𝐺𝑧𝐷 Dittus-Boelter ̅̅̅̅̅̅ 𝑁𝑢𝐷 = 0.023𝑅𝑒𝐷0.8 𝑃𝑟 𝑛 ̅̅̅̅̅̅ 𝑁𝑢𝐿 = 0.68 𝑃𝑟 0.5 𝐺𝑟𝐿0.25 (0.952 + 𝑃𝑟)0.25 ̅̅̅̅̅̅ 𝑁𝑢𝐿 = 0.13 𝑅𝑎𝐿 1/3 ̅̅̅̅̅̅̅ 𝑁𝑢𝐿𝑐 = 0.54 𝑅𝑎𝐿𝑐 1/4 -Properties at 𝑇̅ = at 𝑇𝑠 -Turbulent regime -Properties at ̅̅̅̅ 𝑇𝑚 = -Laminar, developed 2 𝑇 +𝑇𝑚,𝑜 𝑇 +𝑇𝑚,𝑜 -Properties at ̅̅̅̅ 𝑇𝑚 = 𝑚,𝑖 2 -max 25% error -𝑛 = 0.3 for 𝑇𝑠 < 𝑇𝑚 𝑛 = 0.4 for 𝑇𝑠 > 𝑇𝑚 𝑇 +𝑇 -Properties at 𝑇𝑓 = 𝑠 2 ∞ -Laminar regime 𝑇 +𝑇 -Properties at 𝑇𝑓 = 𝑠 ∞ 2 -Turbulent regime 𝑇 +𝑇 -Properties at 𝑇𝑓 = 𝑠 ∞ 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 -Properties at 𝑇𝑓 = -𝐿𝑐 = ̅̅̅̅̅̅̅ 𝑁𝑢𝐿𝑐 = 0.27 𝑅𝑎𝐿𝑐 1/4 𝑇𝑚,𝑖 +𝑇𝑚,𝑜 -Properties at ̅̅̅̅ 𝑇𝑚 = 𝑚,𝑖 2 -Thermal entry length -𝐿𝑐 = ̅̅̅̅̅̅̅ 𝑁𝑢𝐿𝑐 = 0.15 𝑅𝑎𝐿𝑐 1/3 𝑇𝑖𝑛 +𝑇𝑜𝑢𝑡 except 2 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 -Properties at 𝑇𝑓 = -𝐿𝑐 = 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 2 𝑇𝑠 +𝑇∞ 2 𝑇𝑠 +𝑇∞ 2 𝑃𝑟𝑠

Homework Materials - Convection Correlations

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Homework Materials - Convection Correlations

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