We all scream for ice cream Todd Nelson Kendall Thacker ME 340 Semester Project Winter 2014
Problem Statement • How long will it take for the outside surface of an ice cream cone to arrive at melting temperature* while walking around? • *Melting occurs at -5.6°C
Procedure • Find properties of air and ice cream at appropriate temperatures • Calculate forced convection coefficient (with Whitaker model) • Use approx transient response model to find the time required to heat outer surface to melting temperature • Perform experiment to validate **Note: All calculations done using MATLab
Problem Parameters 0.1016 meters Walking Speed V=.9 m/s Ice Cream Properties* K=0.9 w/m°C Melts at T=-5.6°C Initial Temp= -6°C Specific Heat (Cp)=2.75 KJ/kgK Inside Air T=21.3°C • **Thermophysical properties for ice cream , 2006 ASHRAI Handbook for Refrigeration http://pcfarina.eng.unipr.it/Public/Termofluidodinamica/Utility/Tabelle%20Alimenti.pdf
Analytical Results • Time to melt= 7.15 minutes • Convection coefficient= 756 W/mk (**Fourier number is 0.07 and the model requires 0.1 or greater to be accurate. Use with caution) • Assumptions: • No radiation effects (eating indoors) • Ice cream geometry is approximated as a sphere • Walking is at constant rate • Previously melted ice cream running down the sides does not effect the heat transfer rate • Ice cream is not being eaten during test • Properties of ice cream are accurate
Experimental Results & Discussion Experiment was performed by purchasing chocolate ice cream cone from Cougar Eat and walking around at a steady rate. • Time to melt=15 minutes (time to outside surface is completely melted) Discussion • The error between the analytical and experiment results could be due to over simplified problem setup. For more accurate results, the effect of the melted ice cream on the un-melted portion needs to be accounted for.
References • Fundamentals of Heat and Mass Transfer 7th edition, Bergman, Lavine, Incropera, Dewitt • Thermophysical properties for ice cream , 2006 ASHRAI Handbook for Refrigeration http://pcfarina.eng.unipr.it/Public/Termofluidodinamica/Utility/Tabelle%20Alimenti.pdf Equipment Used • Infrared temp sensor to measure surface temperature of ice cream • Thermocouple to measure ambient air temperature • Matlab 2014