Lumped Capacitance Analysis of Steak

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Lumped Capacitance Analysis of Steak

• By Steven Brewer and Tyler Christiansen

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Problem

• We wanted to determine if a steak could be cooked
  in the oven to various degrees of cooking (rare,
  medium, medium-well, and well done) using time
  estimates derived from the lumped capacitance
  method
• Temperatures for the center of the steak at each
  degree of cooking were found online

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Test Setup

• Thermocouple
• Steaks (0.1m by 0.05m by 0.02m)
• Oven at 305 F

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Test Setup
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Test Setup
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Procedure

• Calculate convection coefficient of the oven
• Measure temperature difference in the oven
• Calculate values of Ra, Nu, and h
• Calculate time for steak to reach temperature of
  desired degree of cooking
• Rare 125 F
• Medium 145 F
• Medium well 155 F
• Well done 165 F

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Procedure (cont.)

• Cook steaks in oven at 305 F for estimated time
  to reach desired temperature
• Rare 42.6 min
• Medium 55.3 min
• Medium well 61.6 min
• Well done 69.7 min
• Take data at each interval with thermocouple
• Calculate error

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Assumptions

• Steak is modeled by rectangular enclosure under
  free convection
• Radiation, conduction negligible
• Uniform convection from top to bottom of oven
• Lumped capacitance method

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Calculate Convection Coefficient
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Calculate Time to Desired Temperature
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Calculate Biot Number
Bi ?LC/k Bi ?(V/A)/k Bi
4.137(.0001/.016)/.480 Bi 0.054 lt .1
(Lumped capacitance is valid)
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Data Acquisition
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Results
Rare Medium Medium Well Well Done
Initial Temp T0 (K) 277 277 277 277
Desired temp T (K) 325 336 341 347
Time to T (min) 42.6 55.3 61.6 69.7
Tmeas (K) 324.1 332.9 336.8 341.1
error 0.28 0.92 1.23 1.70
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Conclusions

• The lumped capacitance method is extremely
  accurate in predicting time to cook a steak and
  necessary temperatures
• Assumptions and calculations were very close to
  measured values
• Error of less than 2 for all degrees of cooking
• A steak could almost be cooked using lumped
  capacitance, but would need more time than
  estimated to ensure safety

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Acknowledgements

• Torstveit, A.K., Effect of Packaging on Chilling
  and Temperature Control, http//www.nordicfoodpack
  .org/16027.
• Steak, Wikipedia, http//en.wikipedia.org/wiki/Ste
  ak.
• Incoprera, et al., Fundamentals of Head and Mass
  Transfer, 6th Ed., 2007.