Heat Transfer Lecture: Radiation

Introduction

• Focus on radiation, the third mode of heat transfer.
• Other modes: conduction and convection.
• Reminder: Heat transfer is driven by a temperature difference.

Modes of Heat Transfer

1. Conduction
   • Heat moves through a solid.
   • Driven by a temperature gradient.
2. Convection
   • Heat transfer with fluid motion.
   • Driven by an algebraic temperature difference (T1 - T∞).
3. Radiation
   • Heat transfer from one surface to another via electromagnetic waves.
   • Stephan-Boltzmann Law governs the rate equation.

Radiation

• Occurs between surfaces; does not require a medium.
• Heat transfer can happen in a vacuum.
• Example: Feeling heat from a fire is due to radiation, not hot air.
• Like visible light, thermal radiation can be blocked by objects.

Stefan-Boltzmann Law

• Rate of heat transfer depends on:
  • Temperature to the fourth power.
  • Emissivity (ε): surface property affecting heat emission.
  • Stefan-Boltzmann constant (σ): 5.67 x 10^-8 W/m²K⁴.
  • Black body: perfect emitter.

Emissivity

• Affects how much heat is emitted compared to a black body.
• Values range between 0 and 1 (1 being a perfect emitter).

Radiation Heat Transfer

• Emissive Power (E): Energy emitted by a surface.
• Irradiation (G): Energy intercepting a surface.
• Absorptivity (α): Fraction of G absorbed by the surface.
• Simplified formula for heat transfer with large surroundings: [ q_{rad} = \epsilon \sigma (T_s^4 - T_{surroundings}^4) ]

Practical Example

• Consider a roof losing heat by radiation:
  • Roof temp: 35°C, Surroundings: 20°C.
  • Surface area: 50 m², Emissivity (ε) = 0.85.
  • Use Stefan-Boltzmann Law to calculate heat loss.
  • Total rate of radiative heat exchange calculated in watts.

Key Points

• Radiation depends on temperature differences to the fourth power.
• Can occur alongside convection.
• Important at high surface temperatures.
• Simplified form applies to small objects with uniform surroundings.

Summary

• Radiation can transfer energy across a vacuum.
• Understanding requires considering both emissive power and absorption.
• Emissivity and absorptivity are key surface properties.
• The Stefan-Boltzmann law is crucial for calculating heat transfer rates.