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?
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
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
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