Mechanisms of Heat Transfer

Heat transfer occurs through three primary mechanisms: conduction, convection, and radiation. Each plays a crucial role in the movement of thermal energy in different situations.

Conduction

Conduction is the transfer of heat through direct contact between molecules.
It occurs mainly in solids (especially metals) because their atoms are closely packed.
The rate of conduction depends on the thermal conductivity of the material.
Formula:
\[ Q = \frac{kA \Delta T}{d} \]
Example: A metal spoon gets hot when placed in a boiling pot.

Convection

Convection is the transfer of heat in fluids (liquids and gases) due to motion of the fluid itself.
It happens because warmer fluids expand, become less dense, and rise, while cooler fluids sink.
Two types:
1. Natural Convection: Occurs due to density differences (e.g., warm air rising).
2. Forced Convection: Occurs when an external force moves the fluid (e.g., a fan or pump).
Formula:
\[ Q = hA \Delta T \]
Example: Hot air rising above a candle flame.

Radiation

Radiation is the transfer of heat via electromagnetic waves without needing a medium.
All objects emit radiation based on their temperature.
The amount of radiation emitted follows the Stefan-Boltzmann Law:
\[ P = \sigma A T^4 \]
Example: The Sun heating the Earth.

These three modes often work together. For example, a hot cup of coffee conducts heat through the cup, convects heat to the surrounding air, and radiates heat as infrared waves.

A metal rod of length 1.5 m and cross-sectional area 2 cm² has one end maintained at 100°C and the other at 30°C. The thermal conductivity of the metal is 200 W/m·K. Find the rate of heat transfer through the rod.

Convert units:

\(A = 2 \times 10^{-4} \, \text{m}^2, \quad \Delta T = 70^\circ C, \quad d = 1.5 \, \text{m}\)

\(Q = \frac{200 \times 2 \times 10^{-4} \times 70}{1.5} = 1.87 \, \text{W}\)

If the Sun’s surface temperature is 5800 K and it emits radiation like a black body, what is the peak wavelength of its radiation?

Using Wien’s law:

\(\lambda_{\text{max}} T = 2.9 \times 10^{-3} \, \text{m·K}\Rightarrow \lambda_{\text{max}} = \frac{2.9 \times 10^{-3}}{5800} = 500 \, \text{nm}\)

Written by Thenura Dilruk