Explain in detail the different modes of heat transfer with suitable examples.

Heat transfer is a fundamental concept in Food Processing and Engineering, playing a critical role in the preservation, cooking, drying, freezing, and sterilization of food products. The three primary modes of heat transfer are conduction, convection, and radiation. Each mode operates under different principles and conditions, making them suitable for various food processing applications.

1. Conduction:

Conduction is the transfer of heat through a solid material or between objects in direct contact. It occurs due to the vibration and interaction of molecules within the material. In conduction, heat flows from the region of higher temperature to the region of lower temperature without any movement of the material itself. The rate of heat transfer by conduction is governed by Fourier's Law:

\[
q = -k \cdot A \cdot \frac{dT}{dx}
\]

where:
- \(q\) is the rate of heat transfer (W),
- \(k\) is the thermal conductivity of the material (W/m·K),
- \(A\) is the cross-sectional area (m²),
- \(\frac{dT}{dx}\) is the temperature gradient (K/m).

Example: 
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