For heat transfer purposes, an egg can be considered to be a 5.5-cm-diameter sphere having the p

step 1 Our question is, an ordinary egg can be approximated as a 5 .5 centimeter diameter sphere. The e

For heat transfer purposes, an egg can be considered to be a...

For heat transfer purposes, an egg can be considered to be a $5.5-\mathrm{cm}$-diameter sphere having the properties of water. An egg that is initially at $8^{\circ} \mathrm{C}$ is dropped into the boiling water at $100^{\circ} \mathrm{C}$. The heat transfer coefficient at the surface of the egg is estimated to be $800 \mathrm{~W} / \mathrm{m}^2$ - ${ }^{\circ} \mathrm{C}$. If the egg is considered cooked when its center temperature reaches $60^{\circ} \mathrm{C}$, determine how long the egg should be kept in the boiling water.

Key Concepts

Transient Conduction

Transient conduction refers to the time-dependent process of heat transfer within a body as it moves towards thermal equilibrium with its surroundings. In such problems, the temperature of the object changes with both space and time until it reaches the temperature of its environment, or another specified condition in cases like heating or cooling processes.

Convective Heat Transfer Coefficient

This coefficient quantifies the heat transfer between a solid surface and a fluid moving over the surface. It plays a crucial role in determining the rate of heat entering or leaving an object by convection. In problems like these, it is used in conjunction with Newton’s law of cooling, which relates the heat transfer rate to the temperature difference between the object's surface and the fluid.

Thermal Properties

Thermal properties such as density, specific heat, and thermal conductivity define how a material responds to heat transfer. When solving transient heat conduction problems, these properties determine the material’s thermal diffusivity, which in turn affects the rate at which temperature changes occur within the object. In many practical problems, approximating an object's properties to match those of water can simplify the calculations.

Lumped Capacitance Method

This method is used when the internal resistance to heat conduction within an object is negligible compared to the resistance at the surface due to convection. The approach assumes a uniform temperature throughout the object during the heating or cooling process, leading to an exponential change in temperature with time. It simplifies the analysis of transient heat conduction by reducing the problem to a single ordinary differential equation based on energy conservation.

Biot Number

The Biot number is a dimensionless parameter that compares the internal conduction resistance within a body to the external convective heat transfer resistance. A small Biot number (typically less than 0.1) indicates that the lumped capacitance method is applicable because the temperature gradients inside the body are minimal. It is defined as the product of the convective heat transfer coefficient and a characteristic length divided by the thermal conductivity of the solid.

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