1. Lumped Capacitance Analysis of Steak By Steven Brewer and Tyler Christiansen

2. 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

3. Test Setup  Thermocouple  Steaks (≈0.1m by 0.05m by 0.02m)  Oven at 305° F

4. Test Setup

6. 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

7. 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

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

9. Calculate Convection Coefficient

10. Calculate Time to Desired Temperature

11. Calculate Biot Number Bi = ЋL C /k Bi = [Ћ*(V/A)]/k Bi = [4.137*(.0001/.016)]/.480 Bi = 0.054 <.1 (Lumped capacitance is valid)

12. Data Acquisition

13. Results RareMediumMedium WellWell Done Initial Temp T 0 (K) 277 Desired temp T (K) 325336341347 Time to T (min) 42.655.361.669.7 T meas (K) 324.1332.9336.8341.1 % error 0.280.921.231.70

14. 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

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