PUMPKIN GUTS
ME 340 Heat & Mass
Transfer
FINAL PROJECT
Authors:
Jessica Bauer
&
Marina Samuels
Cooking Problems
• 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.
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The Model
• Lumped Capacitance 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
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Dimensions
H
D
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4
Finding Properties
• We calculated a weighted average to find cp and densities
Cp of Crust
sugar
Specific Heat
[kJ/(kg-°C)]
1.59
1.67
3.93
1.256
Amt. in Crust
[cups]
1.5
0.5
0.0417
0.0417
salt
0.88
0.0208
total
1.66
2.0834
Item
flour
oil
milk
Cp of Pumpkin
[kJ/(kg-°C)]
% of crust
0.719977
0.2399923
0.0200154
0.0200154
0.0099837
3.85
Cp of Pie
Item
Crust
Filling
Total
% Volume
0.135
0.865
1
Cp
1.66
3.85
3.55435
Density of Pie
Density of Crust
545.3
Density of Pumpkin
1035.55
ME 340 Heat & Mass Transfer
Item
% Volume
Density
Crust
0.135
545.3
Filling
0.865
1035.55
Total
1
969.36625
5
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
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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
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Temperature vs Time
Time in Oven VS Temp of Pie
420
400
temp [K]
380
360
340
320
300
280
0
20
40
60
time [min]
80
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120
8
Problem Solved
• 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
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9
Sources
density of pumpkin - http://www.aqua-calc.com/page/density-table
specific heat of pumpkin and flour - http://www.engineeringtoolbox.com/specificheat-capacity-food-d_295.html
density of crust - http://www.aqua-calc.com/page/density-table
specific heat of oil, milk - http://www.engineeringtoolbox.com/specific-heat-fluidsd_151.html
specific heat of salt - http://www.engineeringtoolbox.com/specific-heat-solidsd_154.html
specific heat of cane sugar (close to sugar) http://www.armstronginternational.com/files/common/allproductscatalog/cg53.pdf
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