1. Lumped Burrito Using Lumped Capacitance to Cook a Frozen Burrito Chad Pharo & Chris Howald ME EN 340 Heat Transfer Project

2. Objective 5/8/20152  In ME EN 340, we have to make many assumptions for our homework problems. Lumped capacitance is no exception – several assumptions are made during a typical problem.  For our project, we wanted to see how accurate the lumped capacitance method would be for predicting the cooking time of a frozen burrito. Lumped Burrito

3. Description of Experiment 5/8/20153  We cooked 3 frozen burritos at different temperatures – 300°F, 350°F, and 400°F  The burritos were cooked for the time specified by the lumped capacitance calculations using T final = 165°F  At the end of the time period, we measured the interior temperature of the burrito and compared it to the interior temperature of a burrito cooked with the recommended time and oven temperature. Lumped Burrito

4. Assumptions  Burrito assumed to be a cylinder  T sur = T ∞ for radiation calculations  Only modes of heat transfer considered are free convection, radiation, and conduction through the burrito (ignore conduction through the cooking rack)  Thermophysical properties of burrito were estimated as those of water (Table A-6)… like the quizzes in class  Emissivity value of plaster board was assumed (ε = 0.92) since the outer tortillas are hard  Final temperature of T final = 165°F was chosen based on average food quality standards 5/8/20154Lumped Burrito

5. Calculations Variables Defined 5/8/20155Lumped Burrito L = 0.143 m D = 0.0381 m  Properties of water @ 273 K: ρ = 1000 kg/ m 3 ; k = 0.569 W/m*K ; c p = 4217 J/kg*K ; α = 1.3493e-7 m 2 / s  T i = 0°F = 255.37 K  T∞,1 = 300°F = 422.04 K  T∞,2 = 350°F = 449.82 K  T∞,3 = 400°F = 477.59 K  T film,1 = 338.71 K  T film,2 = 352.60 K  T film,3 = 366.48 K

6. Calculations Equations Used  Free Convection:  Radiation: 5/8/20156Lumped Burrito

7. Calculations Equations Continued  Biot Number:  Lumped Capacitance: 5/8/20157Lumped Burrito

8. Carrying Out the Experiment… 5/8/20158Lumped Burrito Lumped Capacitance Burrito @ 400°F was crispy on the outside Burrito @ recommended settings burst in the oven (too hot for too long) Internal temperature was measured with food thermometer

9. Results 5/8/20159Lumped Burrito

10. Conclusions  We did not reach the desired T final = 165°F using the lumped capacitance model; however, the burritos were still an acceptable temperature for consumption.  The lumped capacitance results (in our opinion) were better than the recommended package directions because the package directions caused the burrito to burst open inside the oven.  Overall, the lumped capacitance method is an acceptable way to cook a frozen burrito. 5/8/201510Lumped Burrito

11. FYI… 5/8/201511Lumped Burrito

12. Appendices (Hand Calculations) 5/8/2015Lumped Burrito12

13. Appendices 5/8/201513Lumped Burrito

14. 5/8/2015Lumped Burrito14 Iteration 1 Iteration 2Iteration 3

15. 5/8/2015Lumped Burrito15 Actual temperatures Lumped Capacitance times