PUMPKIN GUTS

ME 340 Heat & Mass Transfer

FINAL PROJECT

Authors: Jessica Bauer

&Marina Samuels

2ME 340 Heat & Mass Transfer

• Marina loves homemade chocolate chip cookies but every time she put them in the oven they always end up a little bit burned.

• When it came time for Thanksgiving, Marina wanted to make a pumpkin pie for her sister, who loves pumpkin pie.

• Unfortunately, Marina didn’t know how to overcome her cooking problem.

• Her good friend Jess had just the solution.

Cooking Problems

3ME 340 Heat & Mass Transfer

• Lumped Capacitance Model:

The Model

• Assumption: The thin metal container, the pie crust, and the pumpkin pie filling are approximated as a short cylinder of one solid material that is spatially uniform

• Reminder: The temperature is a function of time only

4ME 340 Heat & Mass Transfer

DimensionsH

D

5ME 340 Heat & Mass Transfer

Finding Properties

• We calculated a weighted average to find cp and densitiesCp of Crust

Item Specific Heat [kJ/(kg-°C)]

Amt. in Crust [cups]

% of crust

flour 1.59 1.5 0.719977oil 1.67 0.5 0.2399923

milk 3.93 0.0417 0.0200154sugar 1.256 0.0417 0.0200154

salt 0.88 0.0208 0.0099837

total 1.66 2.0834

Density of PieItem % Volume Density

Crust 0.135 545.3

Filling 0.865 1035.55

Total 1 969.36625

Cp of PieItem % Volume Cp

Crust 0.135 1.66Filling 0.865 3.85Total 1 3.55435

Density of Crust 545.3

Density of Pumpkin 1035.55

Cp of Pumpkin [kJ/(kg-°C)] 3.85

6ME 340 Heat & Mass Transfer

Finding h

• In order to find the exterior flow h, we modeled the cylinder as a horizontal flat plate of characteristic length L = As/P = D/4

7ME 340 Heat & Mass Transfer

Finding t

• Back to the lumped capacitance model: We are looking for the exact amount of time t that Marina should bake the pumpkin pie in the oven

8ME 340 Heat & Mass Transfer

Temperature vs Time

0 20 40 60 80 100 120280

300

320

340

360

380

400

420Time in Oven VS Temp of Pie

time [min]

tem

p [K

]

9ME 340 Heat & Mass Transfer

• If the pie crust needs to reach 400K (260.6⁰F), the graph lists t = 4440 sec = 74 minutes, which is close to recipe instructions so we know our model is valid

• Now Marina can cook perfect pumpkin pie for her sister

Problem Solved

10ME 340 Heat & Mass Transfer

density of pumpkin - http://www.aqua-calc.com/page/density-tablespecific heat of pumpkin and flour - http://www.engineeringtoolbox.com/specific-heat-capacity-food-d_295.htmldensity of crust - http://www.aqua-calc.com/page/density-tablespecific heat of oil, milk - http://www.engineeringtoolbox.com/specific-heat-fluids-d_151.htmlspecific heat of salt - http://www.engineeringtoolbox.com/specific-heat-solids-d_154.htmlspecific heat of cane sugar (close to sugar) - http://www.armstronginternational.com/files/common/allproductscatalog/cg-53.pdf

Sources