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PUMPKIN GUTS

Learn how to bake the perfect pumpkin pie using the lumped capacitance model in ME 340 Heat & Mass Transfer. This model calculates the optimal baking time based on temperature and time variations, ensuring your pie turns out just right every time.

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PUMPKIN GUTS

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  1. PUMPKIN GUTS ME 340 Heat & Mass Transfer FINAL PROJECT Authors: Jessica Bauer & Marina Samuels

  2. 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. ME 340 Heat & Mass Transfer

  3. 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 ME 340 Heat & Mass Transfer

  4. Dimensions H D ME 340 Heat & Mass Transfer

  5. Finding Properties • We calculated a weighted average to find cp and densities ME 340 Heat & Mass Transfer

  6. 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 ME 340 Heat & Mass Transfer

  7. 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 ME 340 Heat & Mass Transfer

  8. Temperature vs Time ME 340 Heat & Mass Transfer

  9. 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 ME 340 Heat & Mass Transfer

  10. Sources density of pumpkin - http://www.aqua-calc.com/page/density-table specific heat of pumpkin and flour - http://www.engineeringtoolbox.com/specific-heat-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-fluids-d_151.html specific heat of salt - http://www.engineeringtoolbox.com/specific-heat-solids-d_154.html specific heat of cane sugar (close to sugar) - http://www.armstronginternational.com/files/common/allproductscatalog/cg-53.pdf ME 340 Heat & Mass Transfer

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