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Lumped Capacitance for meats

Timothy Jackman , Matthew Barg , Emily Peterson ME 340. Lumped Capacitance for meats. We were interested in verifying the accuracy of the lumped capacitance model for steak, chicken, and hamburger. Project description. 1 Electric Oven @ 450 K (350°F) 1 Thermocouple 1 Timer. Test setup.

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Lumped Capacitance for meats

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  1. Timothy Jackman, Matthew Barg, Emily Peterson ME 340 Lumped Capacitance for meats

  2. We were interested in verifying the accuracy of the lumped capacitance model for steak, chicken, and hamburger. Project description

  3. 1 Electric Oven @ 450 K (350°F) 1 Thermocouple 1 Timer Test setup

  4. Air @ 450 K • ρ = 0.774 kg/m3 • cp= 1.021 KJ/kg K • μ = 250.7 E-7 N s/m2 • ν = 32.39 E-6 m2/s • k = 37.3 E-3 W/m K • α = 47.2 E-6 m2/s • Pr = .686 • β = 2.22 E-3 K-1 Convective Coefficient Calculations • We measured the temperature difference between the top and bottom coils in the oven and used Incropera equation 9.49 to determine the convective coefficient. T1-T2 = 290 K RaL = gβ(T1-T2)L3/αν RaL = (9.81)(2.22 E-3)(290)(0.432)3 (47.2 E-6)(32.39 E-6) RaL = 3.327 E8 Ћ = k(0.069RaL1/3)(Pr0.074)/L Ћ = (37.3 E-3)(0.069)(3.327 E8)1/3(0.686)0.074/0.432 Ћ = 4.01 W/m2 K

  5. Meat Properties

  6. Our goal was to compare the actual temperature increase in the meat over eight minutes compared to the estimated temperature increase using Lumped Capacitance. Test Procedure

  7. We measured the initial temperature of the meat and placed it in the oven at constant temperature. After eight minutes, we measured the internal temperature of the meat at the center. Test procedure

  8. Lumped Capacitance is a valid model. • Incropera equation 9.49 is valid: • Convective coefficient model was valid for L/H << 1, while our L/H = 17/22. • We assumed the temperature difference in the coils was the temperature difference of the enclosure. • The oven was at a constant temperature. Assumptions

  9. Calculate the Biot number to confirm that Lumped Capacitance can be used. Lumped Capacitance confirmation Bi = ЋLc/k Bisteak = 0.051 Bihamburger = 0.081 Bichicken = 0.051 Bi < 0.1 so lumped capacitance may be used for all meats

  10. Lumped Capacitance Equations T(t) = T∞ + (To - T∞)exp(-ЋAst/ρcpV) For chicken: T(480s) = 450 + (290-450)exp[-(480)(4.01)(1.508 E-2)/(1000)(1.560)(9.29 E-5)] T(480s) = 322.2 K

  11. Lumped capacitance results

  12. Lumped capacitance accurately predicted the temperature of the meats after 8 mins. Error of 1–6.9% was obtained from this experiment. Conclusion

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