A S TUDY OF H EAT T RANSFER TO C ARROTS Brettany Rupert Brett Rowberry Fall 2011

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

Assumptions 1.Lumped capacitance is not valid. Use transient conduction. 2.Temperature of boiling water is constant. 3.Heat capacitance (c p ) of the carrot is similar to that of water (a carrot is 89% water). Thermal conductivity of the carrot (k) is 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:

Experimental Design 1.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 Data 1.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 Θ 0 * =C 1 exp(-ζ 1 2 Fo)=(T-T ∞ )/(T i - T ∞ )

Calculations from Data cont. 3.Use the coefficients found in the best fit curve to estimate C 1 and ζ 1. 4.Use C 1 and ζ 1 to estimate Biot number. 5.Use Biot number to calculate heat transfer coefficient, given k= W/m∙K. h = 2280 W/m 2 ∙K

Conclusion Analytically we found h = 1460 W/m 2 ∙K and experimentally we found h = 2280 W/m 2 ∙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 /view/2883