Lumped Capacitance Analysis of Steak By Steven Brewer and Tyler Christiansen 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 Test Setup Thermocouple Steaks (0.1m by 0.05m by 0.02m) Oven at 305 F Test Setup Test Setup
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 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 Assumptions Steak is modeled by rectangular enclosure under free convection Radiation, conduction negligible Uniform convection from top to bottom of oven Lumped capacitance method Calculate Convection
Coefficient Calculate Time to Desired Temperature Calculate Biot Number Bi = LC/k Bi = [*(V/A)]/k Bi = [4.137*(.0001/.016)]/.480 Bi = 0.054 < .1 valid)
(Lumped capacitance is Data Acquisition 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 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 Acknowledgements Torstveit, A.K., Effect of Packaging on Chilling and Temperature Control, http://www.nordicfoodpack.org/16027.
Steak, Wikipedia, http://en.wikipedia.org/wiki/Steak. Incoprera, et al., Fundamentals of Head and Mass Transfer, 6th Ed., 2007.
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