Cooking Chicken

1
Cooking Chicken
Andrew Davidson April 4, 2014 ME 340 Heat
Transfer Winter 2014
2
Description objectives

• Measure the time to cook chicken in boiling water
  when internal temperature reaches 74C
• Model experiment using both the lumped
  capacitance and transient conduction analytical
  methods in MATLAB
• Compare actual cook time to the estimated time
  provided by each model

3
Experiment set up

• Materials
• Calibrated thermocouple
• Pot of boiling water kept at a constant
  temperature of 87C
• 3 chicken breasts (no bones) in a cylindrical
  shape 6cm long x 3cm diameter and thawed to
  15C
• Timer
• Home stove

4
experiment
Test T initial ( C) T final ( C) ? Temp Time (sec)
1 15 74.2 59.2 656
2 14.6 74.1 59.5 644
3 14.8 75 60.2 711.2
Average time of 670 seconds to cook chicken
5
Analytical model Assumptions

• Constant temperature of boiling water at 87C
• Chicken shape can be analyzed as infinite
  cylinder
• Chicken has constant properties
• Chickens properties are the same as those of
  water (Table A.6)

Temperatures (C) Temperatures (C)
Ti (inside chicken) 15
Tf (inside chicken) 74
Tave (inside chicken) 44.5
T8 (water) 87
Water Properties at Tave Water Properties at Tave
? (kg/m³) 989
Cp (J/kgK) 4180
k (W/m²) 0.640
Vf (m3/kg) 1.0011 E-3
Vg (m3/kg) 13.98
hfg (kJ/kg) 2390
a (k/?Cp) 15.5 E-6
s(N/m) 0.0683
Chicken Dimensions Chicken Dimensions
Diameter (m) 0.03
Length (m) 0.06
Asurface (m²) 0.0057
Volume (m3) 4.24 E-5
6
Model results

• Lumped Capacitance Method
• q 483233.9 (W/m2) equation 10.6 for boiling
  water
• h 6711.6 (W/m2K) as calculated with heat flux
  value
• Biot Number Calculations
• Bi hLc/k (hro)/(2k)
• Bi 78.7
• Bi gt 0.1 ? lumped capacitance model NOT valid
• Time Predicted
• t 7.91 seconds

All calculations done in MATLAB as shown in the
Appendix below
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Model results

• Transient Conduction
• q 483233.9 (W/m2) equation 10.6 for boiling
  water
• h 6711.6 (W/m2K) as calculated with heat flux
  value
• Biot Number Calculations
• Bi (hro)/(k) 157.3
• Bi ? ?1 , C1 (Table 5.1 in Textbook)
• Time Predicted
• t r2/(a?2) ln?(T8- Ti)/(T8- Tf ) C1J0
  (0)
• Time 548.6 seconds
• Fo (at)/r2 0.38 gt 0.2 ? approximate
  solution is valid

All calculations done in MATLAB as shown in the
Appendix below
8
conclusions

• The lumped capacitance method time prediction was
  significant off from the experiment values
  because the Biot number showed the model was not
  valid.
• The transient conduction method produced a time
  predication that was relatively accurate when
  compared to the experimental values
• Texp 670 sec Tmodel 548.6 sec

9
improvements

• Potential Sources of Error ? Improvement
• Each chicken size was assumed to be the same size
  when they were trimmed to estimate the
  appropriate cylinder, but they were not exact
• Cut chicken to exact sizes measured
• Water was assumed to be at the same temperature
  the whole time, but the pot of water might have
  been small enough to change temperature when the
  chicken was first placed inside
• Use a bigger pot of water to minimize differences
• Chicken properties are not identical to those of
  water
• Use exact values found for chicken
• Variations due to instrumentation used
• Check calibration and run many tests and take
  averages

10
Appendix

• All equations and values used were found in the
  course textbook
• 6th Ed Fund. of Heat and Mass Transfer (Incropera
  et al.)
• MATLAB CODE

Heat Transfer Project - Andrew Davidson -
April 4, 2014 Using both lumped capacitance and
transient conduction methods Chicken Properties
C_Ti 15 C C_Tf 74 C http//www.foodsaf
ety.gov/keep/charts/mintemp.html C_Tave (C_Ti
C_Tf)/2 44.5C 317.5K 320k for properties
for chicken which are the same as water Table
A.6 at 320K for water C_hfg 2390000
J/kg C_vf 1.011(10(-3)) m3/kg C_vg
13.98 m3/kg C_cp 4180 J/kgK C_sigma
0.0683 Nm C_kf 0.640 W/mK Table A.3
for chicken Chicken cooked as a cylinder with
dimensions length 0.06 m (6cm) radius
0.015 m (3cm diameter) volume
lengthpiradius2 m3 C_density 1/C_vf
kg/m3 C_mass C_densityvolume kg As
length2piradius m2
Water Properties Chicken Properties W_hfg
C_hfg kJ/kg W_vf C_vf m3/kg W_vg C_vg
m3/kg W_cp C_cp J/kgK W_sigma C_sigma
Nm W_kf 0.640 W/mK W_Tboil 87 C
Heat Flux Calculations pl 1/W_vf pv
1/W_vg q_flux (0.149)(W_hfg)(pv)(((W_sigma9
.81(pl-pv))/(pv2))(.25)) q'' Eq 10.6 from
book h (q_flux)/(abs(C_Ti-W_Tboil))  
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Appendix

• MATLAB CODE continued

Lumped Capacitance Method (LC) Lc radius/2
Characteristic length for cube (Handout
5.1) Bi_LC (hLc)/C_kf time_LC
((C_densityC_cpvolume)/(hAs))log((W_Tboil -
C_Ti)/(W_Tboil - C_Tf))   Transient
Conduction Method (TC) Bi_TC (hradius)/C_kf
Handout 5.5-5.6 Table 5.1 alpha
C_kf/(C_densityC_cp) Si 2.4050 rad C1
1.6018 time_TC ((radius2)/(alpha(Si2)))
log(((W_Tboil - C_Ti)/(W_Tboil - C_Tf))
(C11))   Check Fo gt 0.2 to be sure model is
valid Fo (alphatime_TC)/(radius2)