timothy jackman, matthew barg, emily peterson me 340
DESCRIPTION
1 Electric 450 K (350°F) 1 Thermocouple 1 TimerTRANSCRIPT
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Timothy Jackman, Matthew Barg, Emily PetersonME 340
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We were interested in verifying the accuracy of the lumped capacitance model for steak, chicken, and hamburger.
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1 Electric Oven @ 450 K (350°F) 1 Thermocouple 1 Timer
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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
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(0.069RaL 1/3)(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
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.
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Density (kg/m3) Cp (kJ/kg K) k (W/m K)
Steak 1,234 3.005 0.480
Hamburger 1,015 3.005 0.380
Chicken 1,000 1.560 0.489
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Our goal was to compare the actual temperature increase in the meat over eight minutes compared to the estimated temperature increase using Lumped Capacitance.
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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.
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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.
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Calculate the Biot number to confirm that Lumped Capacitance can be used.Bi = ЋLc/k
Bisteak = 0.051
Bihamburger = 0.081
Bichicken = 0.051
Bi < 0.1 so lumped capacitance may be used for all meats
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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
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Steak Hamburger ChickenTo (K) 290 289.9 290
V (m3) 9.07E-05 7.68E-05 9.30E-05
As (m2) 0.0148 9.99E-03 1.51E-02
Tmeasured (K) 319 324.5 322.2
Tcalculated (K) 301 302 319
error (%) 5.7 6.9 1.0
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Lumped capacitance accurately predicted the temperature of the meats after 8 mins.
Error of 1–6.9% was obtained from this experiment.