For heat transfer purposes, an egg can be considered to be a 5.5-cm-diameter sphere having the properties of water. An egg that is initially at 4.3°C is dropped into boiling water at 100°C. The heat transfer coefficient at the surface of the egg is estimated to be 800 W/m2⋅K. If the egg is considered cooked when its center temperature reaches 74°C, determine how long the egg should be kept in the boiling water. Solve this problem using the analytical one-term approximation method. The thermal conductivity and diffusivity of the eggs can be approximated by those of water at room temperature to be k = 0.607 W/m·°C and α = 0.146×10−6 m2/s.

The time taken is    

Explanation:

From the question we are told that

   The diameter of the egg is

    The initial temperature of egg the

     The temperature of the boiling water

    The heat transfer coefficient is  

    The  final temperature is

     The  thermal  conductivity of water is

     The diffusivity of the egg

Using one term approximation

We have the

The radius is       Note that this radius is approximation to that of  a real egg

    Now we need to obtain the Biot number which help indicate the value of to use in the above equation

     The Biot number is mathematically represented as

Substituting values  

So for this value  which greater than 0.1 the  coefficient is  

Substituting this into equation 1 we have

Taking natural log of both sides

    The time required for the egg to be cooked is  mathematically represented as

substituting value  is  

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