Lumped Capacitance Analysis of Steak By Steven Brewer

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-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. 1 m by 0. 05 m by 0. 02 m) Oven at 305° F

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 = ЋLC/k Bi = [Ћ*(V/A)]/k Bi = [4. 137*(. 0001/. 016)]/. 480 Bi = 0. 054 <. 1 (Lumped capacitance is valid)

Data Acquisition

Results Rare Medium Well Done Initial Temp T 0 (K) 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, 6 th Ed. , 2007.