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PUMPKIN GUTS ME 340 Heat & Mass Transfer FINAL PROJECT Authors: Jessica Bauer & Marina Samuels Slide 2 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 didnt know how to overcome her cooking problem. Her good friend Jess had just the solution. Cooking Problems Slide 3 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 Slide 4 4ME 340 Heat & Mass Transfer Dimensions H D Slide 5 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 1.591.50.719977 oil 1.670.50.2399923 milk 3.930.04170.0200154 sugar 1.2560.04170.0200154 salt 0.880.02080.0099837 total 1.66 2.0834 Density of Pie Item % Volume Density Crust 0.135545.3 Filling 0.8651035.55 Total 1 969.36625 C p of Pie Item% VolumeCpCp Crust 0.1351.66 Filling 0.8653.85 Total 1 3.55435 Density of Crust545.3 Density of Pumpkin1035.55 Cp of Pumpkin [kJ/(kg-C)] 3.85 Slide 6 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 Slide 7 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 Slide 8 8ME 340 Heat & Mass Transfer Temperature vs Time Slide 9 9ME 340 Heat & Mass Transfer If the pie crust needs to reach 400K (260.6F), 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 Slide 10 10ME 340 Heat & Mass Transfer density of pumpkin - http://www.aqua-calc.com/page/density-tablehttp://www.aqua-calc.com/page/density-table specific heat of pumpkin and flour - http://www.engineeringtoolbox.com/specific- heat-capacity-food-d_295.htmlhttp://www.engineeringtoolbox.com/specific- heat-capacity-food-d_295.html density of crust - http://www.aqua-calc.com/page/density-tablehttp://www.aqua-calc.com/page/density-table specific heat of oil, milk - http://www.engineeringtoolbox.com/specific-heat-fluids- d_151.htmlhttp://www.engineeringtoolbox.com/specific-heat-fluids- d_151.html specific heat of salt - http://www.engineeringtoolbox.com/specific-heat-solids- d_154.htmlhttp://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 http://www.armstronginternational.com/files/common/allproductscatalog/cg- 53.pdf Sources