Boiling an Egg

1. Boiling an Egg Christina Lambertson Winter 2010

2. Description & Objectives By putting an egg in a boiling pot of water find out the following: • Determine how much heat is transferred to the egg. • Use properties to determine the convection coefficient • Determine how much time it takes to cool the egg to a temperature of 65°C. • From wanted final temperature determine convection coefficient • Calculate a time and compare it to the actual time it takes to cool the egg. • Determine the energy transferred to the egg over the time it takes to reach 65°C.

3. Assumptions • Egg is sphere shape. • Properties of the egg can be approximated as those of water. • The process is steady state. • There is no radiation in the process.

4. Problem Set Up Determining heat transfer rate: • Put water into pot and start the boiling process and take temperature of boiling water. • Take egg out of refrigerator and take the initial temperature and put into boiling water. • After a period of about 10 minutes take egg out of water and find the final temperature. • Perform calculations to determine convection coefficient and heat transfer rate.

5. Problem Set Up Determining time and energy transferred: • Put water into pot and start the boiling process and take temperature of boiling water. • Take egg out of refrigerator and take the initial temperature and put into boiling water. Start a timer to determine time taken to heat the egg. • After a period of time take egg out of water and find the temperature at that time. If it is not the desired temperature put back into water and continue to take temperature until desired temperature is reached. • When desired temperature is reached stop the timer. Perform the calculations to determine the convection coefficient and the guess time and compare to the real time taken. • Perform calculations to determine the energy transferred to the egg during the heating process.

6. Results • Heat transfer rate: • q=58.19 W • Time taken to heat the egg to 65°C: • Guess: 17.5 s • Real: 198.2 • Energy transferred to the egg: • Q=1078.47 J

7. Conclusions & Discussion • The heat transfer rate that was calculated seemed to be reasonable for this process. • The time calculated to heat the egg to 65°C was 11 times smaller than what was timed. • I would account the difference in time from that calculated to that timed from the fact that we used properties of water, the shape of an egg is not really a sphere, and there could also be conduction and radiation going on that was not taken into account.

8. Appendix Rate of heat transfer: • Diameter of egg: • D=0.0254 m • Temperatures: • Boiling water: • T∞=95.4°C • Egg: • T0=9.3°C • TF=70.1°C • Acceleration of gravity: • g=9.82 m/s2 • Properties of egg: • Cp=4200 J/kg*K • ρ=969.93 kg/m3 • Pr=2.12 • k=671.4e-3 W/m*k • μ=340e-6 N*s/m2 • α=1.648e-7 m2/s • β=659.1e-6 K-1

9. Appendix Time change and Energy: • Diameter of egg: • D=0.0254 m • Temperatures: • Boiling water: • T∞=95.3°C • Egg: • T0=13.5°C • TF=65°C • Acceleration of gravity: • g=9.82 m/s2 • Properties of egg: • Cp=4179 J/kg*K • ρ=992.06 kg/m3 • Pr=4.37 • k=631.2e-3 W/m*k • μ=660e-6 N*s/m2 • α=1.522e-7 m2/s • β=382.7e-6 K-1

10. Appendix • Equations used: • RaD=g*β*ρ*(Ts-T∞)*D3/(μ*α) • NuD=2+(0.589*Ra1/4)/[1+(0.469/Pr)9/16]4/9 • h=(k/D)*NuD • As=π*D2 • V=π*D3/6 • q=h*As*(T∞-TF) • Bi=h*D/(6*k) • t=[Cp*V*ρ /(As*h)]*ln[(T∞- T0)/(T∞-TF)] • Q=Cp*V*ρ *(T∞- T0)*(1-e[-h*As*t/(Cp*V*ρ)])

11. Appendix • Calculations: • RaD=4.64e7 • NuD=43.5 • h=1149.95 W/m2*K • As=0.002 m2 • V=8.58e-6 m3 • q=58.19 W • Calculations: • RaD=1.84e7 • NuD=40.6 • h=1008.71 W/m2*K • As=0.002 m2 • V=8.58e-6 m3 • t=17.5 s • Q=1078.47 J Heat Transfer Rate: Time change and Energy: