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

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

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

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 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

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

Recorded Experimental Results 6 Total HoursFarenheitKelvin

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

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

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

Appendix A – Transient Conduction Tables 10 Transient t (hours)T(t)F0F0 Valid? t (hours)T(t)F0F0 Valid? FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE

Appendix B – Broth Convection Coefficient & Cooking Time Table 11 h (W/m²*K)Biot Number ζ1ζ1C1t (hours)