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 Dimensions H D

5ME 340 Heat & Mass Transfer Finding Properties We calculated a weighted average to find cp and densities C p of Crust Item Specific Heat [kJ/(kg-°C)] Amt. in Crust [cups] % of crust flour oil milk sugar salt total Density of Pie Item % Volume Density Crust Filling Total C p of Pie Item% VolumeCpCp Crust Filling Total Density of Crust545.3 Density of Pumpkin 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

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 - specific heat of pumpkin and flour - heat-capacity-food-d_295.htmlhttp:// heat-capacity-food-d_295.html density of crust - specific heat of oil, milk - d_151.htmlhttp:// d_151.html specific heat of salt - d_154.htmlhttp:// d_154.html specific heat of cane sugar (close to sugar) pdf 53.pdf Sources