Lumped BurritoUsing Lumped Capacitance to Cook a Frozen

Burrito

Chad Pharo & Chris Howald ME EN 340

Heat Transfer Project

Objective

04/21/23 2

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

04/21/23 3

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

04/21/23 4 Lumped Burrito

CalculationsVariables Defined

04/21/23 5 Lumped Burrito

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:

04/21/23 6 Lumped Burrito

CalculationsEquations Continued

Biot Number:

Lumped Capacitance:

04/21/23 7 Lumped Burrito

Carrying Out the Experiment…

04/21/23 8 Lumped 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

Results

04/21/23 9 Lumped Burrito

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.

04/21/23 10 Lumped Burrito

FYI…

04/21/23 11 Lumped Burrito

Appendices

(Hand Calculations) 04/21/23 Lumped Burrito12

Appendices

04/21/23 13 Lumped Burrito

04/21/23 Lumped Burrito14

Iteration 1

Iteration 2 Iteration 3

04/21/23 Lumped Burrito15

Actual temperatures

Lumped Capacitancetimes