A STUDY OF HEAT TRANSFER TO

CARROTS

Brettany RupertBrett Rowberry

Fall 2011

Problem Statement

Find the heat transfer coefficient of boiling water in Reno, NV analytically and empirically.

Assumptions1. Lumped capacitance is not valid. Use transient

conduction.2. Temperature of boiling water is constant.3. Heat capacitance (cp) of the carrot is similar to that

of water (a carrot is 89% water). Thermal conductivity of the carrot (k) is 0.626 W/m K.∙

4. Free convection is the only mode of heat transfer between the water and the carrot.

5. Difference in elevation will not affect the properties of water significantly (except boiling temperature).

6. Carrot is an infinite cylinder.

Calculations

Using free convection for a horizontal cylinder:

h Nuk

D 1.46 10

3W

m2K

h Nuk

D 1.46 10

3W

m2K

Experimental Design1. Refrigerate carrots.2. Use a stamp scale to measure the

mass of the carrot.3. Measure the length and diameter of

the carrot using calipers.4. Using the thermocouple, measure the

temperature of the boiling water.5. Drill a hole in the baby carrot.6. Place thermocouple probe in the hole.7. Place prepared carrot in boiling water.8. In set time intervals, record the

temperature measured by the thermocouple inside the carrot.

Experimental Data

Calculations from Data1. Use equation 5.49c to plot non-dimensional

temperature vs. time. The data is truncated at 60 seconds to reduce error.

2. Get a best fit curve.

Equation 5.49c

Θ0*=C1•exp(-ζ1

2Fo)=(T-T∞)/(Ti- T∞)

Calculations from Data cont.3. Use the coefficients found in the best fit

curve to estimate C1 and ζ1.

4. Use C1 and ζ1 to estimate Biot number.

5. Use Biot number to calculate heat transfer coefficient, given k= 0.626 W/m K.∙

h = 2280 W/m2 K∙

ConclusionAnalytically we found h = 1460 W/m2 K and ∙experimentally we found h = 2280 W/m2 K. This is ∙an error of 49%. These errors may have come from:•Human error in the experiment•Assumption that free convection is the only mode of heat transfer•Assumption that carrot is an infinite cylinder•Assumption that standard laboratory conditions for pressure are accurate•Inaccurate heat transfer parameters due to uncertainty in carrot properties

References

Incropera, DeWitt, Bergman, Lavine. (2007). Fundamentals of Heat and Mass Transfer. United States of America: John Wiley & Sons.

Manalu, L., Abdullah, K. (1998) . Prediction of Thermal Diffusivity and Conductivity of Carrot. Buletin Keteknikan Pertanian,12(2). Retrieved from

http://journal.ipb.ac.id/index.php/bultek/article/view/2883