An egg, which for the purposes of this problem can be assumed to be a 5-cm-diameter sphere having the thermal properties of water, is initially at a temperature of 4°C. It is immersed in boiling water at 100°C for 15 min. The heat transfer coefficient from the water to the egg may be assumed to be 1700 W/(m2 K). What is the temperature of the egg center at the end of the cooking period?

Question

GIVEN

An egg is immersed in boiling water

Initial temperature (To) = 4°C

Temperature of boiling water (T?) = 100°C

Time that the egg is in the water (t) = 15 min. = 900 s

The heat transfer coefficient (hc) = 1700 W/(m2 K)

FIND

The temperature of the egg center at the end of the cooking period

ASSUMPTIONS

The egg is a sphere of diameter (D) = 5 cm = 0.05 m

The egg has the thermal properties of water



SKETCH

Answer 1

The Biot number for the egg is



Therefore, the internal resistance is significant. Approximate solution can be used to solve the problem. The Fourier number at t = 900 s is



Using approximate solution, we have



For the center r=0, the term becomes indeterminate, so using L Hospital’s rule we get.



For Bi=62.3 which can be considered ? sphere we have