Note You will need to use a spreadsheet to plot data but be careful to make the

Note you will need to use a spreadsheet to plot data

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Note: You will need to use a spreadsheet to plot data, but be careful to make the plot fit an appropriate equation so that you can find h from a trendline fit to the graph. Spreadsheet has calculations, and is used to find h. The blue data are for no fan, the red for with a fan. The equations give slopes which must match -hA/mc p Both equations should have been forced to go through the origin, since the theoretical equation has no intercept when plotted this way. (Note: I converted the data into a linear plot; it is possible to leave with a ln or exp, as long as a different fit is used). A = 4 * pi * r 2 = 4 * pi * 0.0125^2 = 0.00196 m 2 m = 4/3 * pi * r 3 * density = 4/3 * pi * (0.0125)^3 * 8933 = 0.0731 kg density = 8933 kg/m 3 c p = 385 J/kg-K With no fan, hA/mc p = 0.0134 s -1 = h* 0.00196m 2 / {0.0731 kg * 385 J/kg-K) h (no fan) = 192 W/m 2 K With the fan, hA/mc p = 0.0281 s -1 = h* 0.00196m 2 / {0.0731 kg * 385 J/kg-K) h (fan)= 403 W/m 2 K Problem 7 Time (sec) Data Temp, C (no fan) Temp, C (fan) 0.0 185 185 2.0 180 176 4.0 175.5 168 6.0 171.2 160.5 8.0 167.1 153.6 10.0 163.2 147 12.0 159.4 140.8 14.0 155.7 134.4 16.0 152 128.3 18.0 149.1 122.4 20.0 146.4 116.8 22.0 143.8 111.6 24.0 141.3 106 26.0 138.9 101.3 28.0 136.6 97 30.0 134.4 93.1 no fan fan no fan fan no fan fan T-Tinf T-Tinf (T-Tinf)/(Ti-Tinf) (T-Tinf)/(Ti-Tinf) Time (sec) ln{(T-Tinf)/(Ti-Tinf)} ln{(T-Tinf)/(Ti-Tinf)} 160 160 1 1 0 0 0 155 151 0.96875 0.94375 2 -0.031748698 -0.057893978 150.5 143 0.940625 0.89375 4 -0.061210731 -0.112329185 146.2 135.5 0.91375 0.846875 6 -0.090198268 -0.166202175 142.1 128.6 0.888125 0.80375 8 -0.11864278 -0.218467003 138.2 122 0.86375 0.7625 10 -0.146471904 -0.271152771 134.4 115.8 0.84 0.72375 12 -0.174353387 -0.32330925 130.7 109.4 0.816875 0.68375 14 -0.202269195 -0.380162925 127 103.3 0.79375 0.645625 16 -0.230986729 -0.437536439 124.1 97.4 0.775625 0.60875 18 -0.254086123 -0.496347605 121.4 91.8 0.75875 0.57375 20 -0.276082937 -0.555561518 118.8 86.6 0.7425 0.54125 22 -0.297732408 -0.613874 116.3 81 0.726875 0.50625 24 -0.319000756 -0.680724661 113.9 76.3 0.711875 0.476875 26 -0.339852945 -0.740500877 111.6 72 0.6975 0.45 28 -0.360252765 -0.798507696 109.4 68.1 0.68375 0.425625 30 -0.380162925 -0.854196602 y = -0.0127x - 0.0147 R² = 0.9945 y = -0.0285x + 0.0082 R² = 0.9992 y = -0.0134x R² = 0.9902 y = -0.0281x R² = 0.9989 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0 10 20 30 40 ln{(T-Tinf)/(Ti-Tinf)} Time (sec) Series1 Series2 Linear (Series1) Linear (Series2) Linear (Series1) Linear (Series2)
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