lumped burrito using lumped capacitance to cook a frozen burrito chad pharo & chris howald me en...
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Lumped BurritoUsing Lumped Capacitance to Cook a Frozen
Burrito
Chad Pharo & Chris Howald ME EN 340
Heat Transfer Project
Objective
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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
Description of Experiment
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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 Tfinal = 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
Assumptions
Burrito assumed to be a cylinder
Tsur = 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 Tfinal = 165°F was chosen based on average food quality standards
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CalculationsVariables Defined
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L = 0.143 m
D = 0.0381 m
Properties of water @ 273 K: ρ = 1000 kg/ m3 ; k = 0.569 W/m*K ; cp = 4217 J/kg*K ; α = 1.3493e-7 m2 / s
Ti = 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 Tfilm,1 = 338.71 K Tfilm,2 = 352.60 K
Tfilm,3 = 366.48 K
CalculationsEquations Used
Free Convection:
Radiation:
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CalculationsEquations Continued
Biot Number:
Lumped Capacitance:
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Carrying Out the Experiment…
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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
Results
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IterationOven Temperature
(°F)Cooking Time
(minutes)Actual Final Temperature
(°F)1 300 30 1382 350 23 1203 400 19 124
4 375 30 1745 375 45 176
Package Cooking Instructions
Lumped Capacitance Cooking Method
Conclusions
We did not reach the desired Tfinal = 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.
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FYI…
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Appendices
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Appendices
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Iteration 1
Iteration 2 Iteration 3
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Actual temperatures
Lumped Capacitancetimes