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Transient Conduction of a Turkey Cooked by: Benjamin Baird & Michael Jarvis 1.

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Presentation on theme: "Transient Conduction of a Turkey Cooked by: Benjamin Baird & Michael Jarvis 1."— Presentation transcript:

1 Transient Conduction of a Turkey Cooked by: Benjamin Baird & Michael Jarvis 1

2 What is the time required to cook a crock pot turkey roast? Objectives: Determine time required to heat a small turkey roast to an internal temperature of 170 ° F (349.8 K) Compare experimental to analytical measurements Eat the deliciously good turkey and be thankful! 2

3 Experimental Problem Set-up Materials: Barbecue Thermometer Clock Crock Pot Turkey Roast [4.34” (0.11m) diameter] 3

4 Analytical Problem Set-up 4 Temperatures (K) T 0 (inside turkey)291 T done (inside turkey)350 T avg (inside turkey)320.5 T ∞ (broth)355 Water Properties @ T avg ρ (kg/m ³ )991 Cp (J/kg*K)4179 μ (N*s/m²)6.37E-04 k (W/m²)6.33E-01 β (K -1 )3.97E-04 PR4.21 α (k/ρ*Cp) 1.53E-07 Turkey Properties Diameter (m)0.11 Volume (m³)7.03E-04 Surface Area (m²)9.56E-03

5 Effect of different Broth Coefficients 5 From varying the convection coefficient, cooking time changes by 20 minutes.  Data in Appendix B

6 Recorded Experimental Results 6 Total HoursFarenheitKelvin 0.0064290.93 0.2579299.26 0.3890305.37 0.62104313.15 0.78115319.26 0.98122323.15 1.28135330.37 1.55144335.37 2.33165347.04 2.40171350.37

7 Transient Conduction & Actual Results 7 Total Cook Time (hours) h=1200W/m²*K1.9 h=100W/m²*K2.1 Experiment2.40  Convection Coefficient data in Appendix A

8 Conclusions & Recommendations What we Learned: The convection coefficient had very little effect on the cook time (though 20 minutes does make a big difference when you are hungry).  Instead of finding it experimentally, we calculated the cook time using the maximum & minimum plausible values. The model was found to be very sensitive to the turkey diameter, & the broth temperature. The Turkey tasted like Thanksgiving should have! What could be done better: Maintain a constant broth temperature; use a bigger bath  This would reduce measurement inaccuracies. 8

9 Equation References Incropera, P.; Dewitt, D.; Bergman, T.; & Lavine, A.. Fundamentals of Heat and Mass Transfer. 6th Ed. Hoboken, NJ: John Wiley & Sons, Inc., 2007. 9

10 Appendix A – Transient Conduction Tables 10 Transient Conduction@h=100W/m²*KTransient Conduction@h=1200W/m²*K t (hours)T(t)F0F0 Valid? t (hours)T(t)F0F0 Valid? 0228.280.00FALSE 0227.000.00FALSE 0.1247.210.02FALSE 0.1247.930.02FALSE 0.2263.310.04FALSE 0.2265.440.04FALSE 0.3277.000.05FALSE 0.3280.090.05FALSE 0.4288.650.07FALSE 0.4292.340.07FALSE 0.5298.560.09FALSE 0.5302.590.09FALSE 0.6306.990.11FALSE 0.6311.160.11FALSE 0.7314.160.13FALSE 0.7318.330.13FALSE 0.8320.260.14FALSE 0.8324.330.14FALSE 0.9325.450.16FALSE 0.9329.340.16FALSE 1329.860.18FALSE 1333.540.18FALSE 1.1333.620.20FALSE 1.1337.050.20FALSE 1.2336.810.22TRUE 1.2339.980.22TRUE 1.3339.530.24TRUE 1.3342.440.24TRUE 1.4341.840.25TRUE 1.4344.490.25TRUE 1.5343.800.27TRUE 1.5346.210.27TRUE 1.6345.480.29TRUE 1.6347.650.29TRUE 1.7346.900.31TRUE 1.7348.850.31TRUE 1.8348.110.33TRUE 1.8349.860.33TRUE 1.9349.140.34TRUE 1.9350.700.34TRUE 2350.010.36TRUE 2.1350.760.38TRUE

11 Appendix B – Broth Convection Coefficient & Cooking Time Table 11 h (W/m²*K)Biot Number ζ1ζ1C1t (hours) 1008.712.991.981.9983 12510.893.041.981.9331 15013.063.061.981.9079 17515.243.071.991.8984 20017.423.081.991.8861 22519.603.0831.991.8825 25021.773.0851.991.8800 27523.953.0871.991.8776 30026.133.091.991.8739 32528.303.0931.991.8703 35030.483.0951.991.8679 37532.663.11.991.8619 40034.843.14152.001.8158 42537.013.14152.001.8158 45039.193.14152.001.8158 47541.373.14152.001.8158 50043.543.14152.001.8158 52545.723.14152.001.8158 55047.903.14152.001.8158 57550.083.14152.001.8158 60052.253.14152.001.8158 62554.433.14152.001.8158 65056.613.14152.001.8158 67558.793.14152.001.8158 70060.963.14152.001.8158 72563.143.14152.001.8158 75065.323.14152.001.8158 77567.493.14152.001.8158 80069.673.14152.001.8158 82571.853.14152.001.8158 85074.033.14152.001.8158 87576.203.14152.001.8158 90078.383.14152.001.8158 92580.563.14152.001.8158 95082.733.14152.001.8158 97584.913.14152.001.8158 100087.093.14152.001.8158 102589.273.14152.001.8158 105091.443.14152.001.8158 107593.623.14152.001.8158 110095.803.14152.001.8158 112597.983.14152.001.8158 1150100.153.14152.001.8158 1175102.333.14152.001.8158 1200104.513.14152.001.8158


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