3 02 01 01 10 20 30 40 lnT TinfTi Tinf Time sec Series1 Series2 Linear Series1

3 02 01 01 10 20 30 40 lnt tinfti tinf time sec

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-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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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, thus I use the values -0.0134 for no fan and -0.0281 for with a fan. (Note: I converted the data into a linear plot; it is possible to solve and plot then curve fit with a ln or exp, as long as an appropriate curve fit (trendline) is used). A = 4 * pi * r 2 = 4 * pi * 0.0155^2 = 0.00302 m 2 m = 4/3 * pi * r 3 * density = 4/3 * pi * (0.0155)^3 * 2702 kg/m 3 = 0.0421 kg density = 2702 kg/m 3 c p = 903 J/kg-K With no fan, hA/mc p = 0.0134 s -1 = h* 0.00302m 2 / {0.0421 kg) * (903 J/kg-K) h (no fan) = 169 W/m 2 K With the fan, hA/mc p = 0.0281 s -1 = h* 0.00302m 2 / {0.0421 kg) * (903 J/kg-K) h (fan)= 354 W/m 2 K Similarly, for water, a third line can be added to the graph: For the water, hA/mc p = 0.0801 s -1 = h* 0.00302m 2 / {0.0421 kg) * (903 J/kg-K) h (water)= 1008 W/m 2 K (higher value than air; as expected) Validate Biot number: Bi = h L c / k use h’s above L c = r/3 = 0.0155 m / 3 = 0.0052 m k = 237 W/m-K air (no fan): Bi = 169 * 0.0052 / 237 = 0.0037 (VALID) air (fan) Bi = 354 * 0.0052 / 237 = 0.0078 (VALID) water Bi = 1008 * 0.0052 / 237 = 0.022 (Still Valid, but the better/higher the convection term, it is possible that lumped capacitance would no longer be valid) y = -0.0127x - 0.0147 R² = 0.9945 y = -0.0134x R² = 0.9902 y = -0.0285x + 0.0082 R² = 0.9992 y = -0.0281x R² = 0.9989 y = -0.0801x R² = 0.9971 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 0 5 10 15 20 25 30 35 ln{(T-Tinf)/(Ti-Tinf)} Time (sec) Series1 Series2 Water Linear (Series1) Linear (Series1) Linear (Series2) Linear (Series2) Linear (Water)
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  • Heat, Heat Transfer, convective heat transfer, Silicon carbide, capacitance model

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