An ordinary egg can be approximated as a 5.5 cm diameter...

An ordinary egg can be approximated as a 5.5 cm diameter sphere whose properties are roughly $k=0.6 \mathrm{~W} / \mathrm{m}$. ${ }^{\circ} \mathrm{C}$ and $\alpha=0.14 \times 10^{-6} \mathrm{~m}^2 / \mathrm{s}$. The egg is initially at a uniform temperature of $8^{\circ} \mathrm{C}$ and is dropped into boiling water at $97^{\circ} \mathrm{C}$. Taking the convection heat transfer coefficient to be $h$ $=1400 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$, determine how long it will take for the center of the egg to reach $70^{\circ} \mathrm{C}$.

Key Concepts

Transient Heat Conduction

This concept deals with how temperature within a material changes over time according to the heat diffusion equation. It incorporates both spatial and temporal variations and is critical for understanding how heat diffuses through objects with complex geometries and boundary conditions.

Spherical Geometries in Heat Transfer

This refers to analyzing heat conduction in objects that approximate the shape of a sphere, which requires solving the heat equation using spherical coordinates. Solutions in this context often involve eigenfunction expansions that respect the radial symmetry of the problem.

Convective Heat Transfer

Convective heat transfer describes the exchange of heat between a solid surface and a fluid in motion, and is typically modeled using Newton’s law of cooling. The convection coefficient in this formulation quantifies the effectiveness of the heat exchange process at the boundary of the solid.

Biot Number

The Biot number is a dimensionless parameter used to compare the internal thermal resistance of a body to the external resistance to heat transfer by convection. It helps determine whether a lumped system analysis is valid or if internal temperature gradients must be considered by solving the full conduction equations.

Fourier Number

The Fourier number is a dimensionless time parameter that relates the rate of heat conduction to the storage of thermal energy. It is integral to analyzing the transient response of a system, indicating how rapidly a material responds to changes in thermal boundary conditions.

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