# HW6Soln - Problem 20.2 Assume that ends are negligible a....

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Problem 20.2 Assume that ends are negligible a. Bismuth Analysis for Vertical and Horizontal Surfaces Vertical Cylinder. δ =Length of cylinder Iterative approach. Guess a surface temperature Use the following correlation for the Nussult number Pr g Pr 3 2 T Gr Ra = = δ ν β 2 27 / 8 16 / 9 6 / 1 Pr 492 . 0 1 387 . 0 825 . 0 + + = Ra Nu L Bismuth Temp (F) Pr β (1/R -1 ) ν (ft 2 /s) k(Btu/hrftF) 700 0.0141 6.20E-05 1.59E-06 8.870 727.5 0.0138 6.28E-05 1.55E-06 9.160 800 0.0129 6.50E-05 1.46E-06 0.392 Vertical Cylinder Q 750 W Q 2559.8 Btu/hr H 0.5 ft D 0.0625 ft Area 0.10 ft 2 Perimeter 0.20 ft T inf 700 F Guess Surface Temp Tsurf 755 F Tfilm 727.5 K δ 0.5 ft Gr 5.76E+09 Ra 7.93E+07 Nu 25.84 h 473.40 Btu/hrft 2 F T calc 755.1 F

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Horizontal Cylinder 2 27 / 8 16 / 9 6 / 1 Pr 559 . 0 1 387 . 0 60 . 0 + + = Ra Nu D Bismuth Temp (F) Pr β (1/R -1 ) ν (ft 2 /s) k(Btu/hrftF) 700 0.0141 6.20E-05 1.59E-06 8.870 721.8 0.0138 6.28E-05 1.55E-06 9.160 800 0.0129 6.50E-05 1.46E-06 0.392 Horizontal Cylinder Q 750 W 2559.8 Btu/hr H 0.5 ft D 0.0625 ft Area 0.10 ft 2 Perimeter 0.20 ft T inf 700 F Guess Surface Temp Tsurf 743.6 F Tfilm 721.8 F δ 0.0625 ft Gr 8.91E+06 Ra 1.23E+05 Nu 4.09 h 598.82 Btu/hrft 2 F T calc 743.5 F b. Hydraulic Fluid Analysis for Vertical and Horizontal Surfaces Insufficient data. Sorry about this guys. Interestingly enough if you plot the data physical properties of the hydraulic fluid it’s not linear. The natural convective value of 2 2 µ βρ g reaches a max value at 150F and drop from there.
Problem 20.4 Assume that ends are negligible (it’s in the problem statement) Problem with the surface temperature changing with time. That means that “h” also changes with time….Yuck! Need to make a plausible assumption Surface temperature changes from 200F to 100F Æ Average surface temp is 150F Since ambient water stays constant at 50F F F F T film 100 2 50 150 = + = Water Temp (F) Pr β (1/R -1 ) ν (ft 2 /s) k(Btu/hrftF) 100 4.5100 1.80E-04

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## This note was uploaded on 09/07/2009 for the course CBME Kinetics & taught by Professor Lobban during the Spring '09 term at The University of Oklahoma.

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HW6Soln - Problem 20.2 Assume that ends are negligible a....

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