1. By Kasey Gillespie and Leonidas Leite You’re Ready, but is your pizza Hot?

2. PROJECT GOALS Model the rate pizza cools down at room temperature Determine if a box lined with a tin foil keeps the pizza warm longer Suggest methods for improving pizza boxes

3. EXPERIMENTAL DESIGN First Experiment Pizza box Pizza Second Experiment Thin foil TC -Heat oven to approximate temperature of Little Caesars’ warming oven (71 degrees C) -Place pizza in oven and allow its temperature to stabilize. -Remove pizza to wooden table at room temperature, insert thermocouple and record data -Two pizzas were used: first pizza in standard box, second pizza lined with foil in box

4. EXPERIMENTAL RESULTS The pizza with foil took 10 minutes longer to cool to 39 C

5. MODELING THE EXPERIMENT WITH NO FOIL FIRST MODEL – Free convection inside of the box Assumptions The whole pizza is a lump—using one set of thermophysical properties is acceptable The box surface temperature is the average temperature of the pizza and the surroundings The thermophysical properties of the pizza could be measured at the average temperature during the time period The pizza is a finite flat plate The analytical method works because Fo >= 0.2 T(x,t) = T inf +(T i -T inf )C 1 cos(ζ 1 x/L)exp(-ζ 1 2 αt/L 2 )

6. COMPARISON OF FIRST MODEL TO EXPERIMENTAL DATA

7. MODELING THE EXPERIMENT WITH NO FOIL SECOND MODEL – Free convection outside of the box Assumptions The whole pizza and box together is a single lump—using one set of thermophysical properties is acceptable The thermophysical properties of the pizza could be measured at the average temperature during the time period The pizza is a finite flat plate The analytical method works because Fo >= 0.2 T(x,t) = T inf +(T i -T inf )C 1 cos(ζ 1 x/L)exp(-ζ 1 2 αt/L 2 )

8. COMPARISON OF SECOND MODEL TO EXPERIMENTAL DATA

9. WHAT DID THE FOIL DO? The foil did not reduce heat transfer due to radiation it actually served as an inhibitor of convective heat transfer Tin foil Insulating Air Less convective heat loss

10. RECOMMENDATIONS Since the foil only acted as an insulation to convection it would be better to use a material that had a lower coefficient of thermal conductivity (K) o Cardboard—the same material as used on the box o Wax paper o Parchment paper Whatever insulation is used, it should sit directly on top of the pizza instead of lining the actual box Little Caesars could offer the extra thermal insulation for an extra 5 cent charge Eat the pizza before it cools down, it tastes better

11. CONCLUSION The second analytical method provided a good model for the experimental data of the non-foil pizza The pizza covered in foil could only be modeled with more complex analytical methods that are beyond the scope of this course Heat loss of the pizza can be decreased by placing a low-cost insulating material on top of the pizza, which would increase customer satisfaction