John is employed by a new food processing plant where eggs are to be boiled in large quantities to produce egg salad. John has been assigned the task of determining the minimum cooking time for the eggs, utilizing his vast knowledge of heat transfer. As a basis of calculation, he assumed that the eggs are perfect spheres with a diameter of 5 cm and uniform material properties (r =1000kg/m²; Cp = 3300 J/(kg-K) and k=0.75 W/(m-K)). The eggs were taken from a cold storage room at 5°C and immediately put into pots of boiling water at 100°C. The convective heat transfer coefficient of the water is h = 1500 W/m°K. For health safety reasons, the plant requires that the entire egg must be at a temperature above 75°C for at least 20 seconds in order for the cooking process to be complete. a. What is the minimum time necessary to cook the egg to company specifications? b. In the testing lab, John forgot to remove a batch of eggs, and they remained in the cooking pot long enough to reach a uniform temperature of 100°C. At that point, John removed one of the eggs and placed it on a counter. The egg is cooled down by being exposed to ambient air at 30°C with a convective heat transfer coefficient of 8W/m°K. Estimate the amount of time it takes for the egg to cool down to 70°C.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.68P

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Question

John is employed by a new food processing plant where eggs are
to be boiled in large quantities to produce egg salad. John has
been assigned the task of determining the minimum cooking
time for the eggs, utilizing his vast knowledge of heat transfer.
As a basis of calculation, he assumed that the eggs are perfect
spheres with a diameter of 5 cm and uniform material properties
(r =1000kg/m'; Cp = 3300 J/(kg K) and k=0.75 W/(m-K)). The
eggs were taken from a cold storage room at 5°C and
immediately put into pots of boiling water at 100°C. The
convective heat transfer coefficient of the water is h = 1500
W/m°K. For health safety reasons, the plant requires that the
entire egg must be at a temperature above 75°C for at least 20
seconds in order for the cooking process to be complete.
a. What is the minimum time necessary to cook the egg to
company specifications?
b. In the testing lab, John forgot to remove a batch of eggs, and
they remained in the cooking pot long enough to reach a
uniform temperature of 100°C. At that point, John removed
one of the eggs and placed it on a counter. The egg is cooled
down by being exposed to ambient air at 30°C with a
convective heat transfer coefficient of 8W/mK. Estimate the
amount of time it takes for the egg to cool down to 70°C.

Expert Solution

Step 1

Write the given data with suitable variables.

$\begin{array}{rcl} d & = & 5 c m = 0.05 m (\frac{100 c m}{1 m}) \\ r & = & 1000 k g / m^{3} \\ c_{p} & = & 3300 J / k g K \\ h_{1} & = & 1500 W / m^{2} K \\ h_{2} & = & 8 W / m^{2} K \\ k & = & 0.75 W / m K \\ T_{i} & = & 5 ° C \\ T & = & 75 ° C \\ T_{\infty} & = & 100 ° C \end{array}$

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