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

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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

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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

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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

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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

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

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

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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

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Results 5/8/20159Lumped Burrito

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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

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FYI… 5/8/201511Lumped Burrito

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

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Appendices 5/8/201513Lumped Burrito

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

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

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