Heat Transfer Lecture: Radiation

Overview

• Three Modes of Heat Transfer: Conduction, convection, and radiation.
• Focus: Today's lecture focuses on radiation as the final mode of heat transfer.

Basics of Radiation

• Radiative Heat Transfer:
  • Occurs from one surface to another via electromagnetic waves.
  • Described by the Stefan-Boltzmann Law.
• Driving Force: A difference in temperature between surfaces.
  • Conduction: Temperature gradient.
  • Convection: Algebraic temperature difference (T1 - T∞).
  • Radiation: Nonlinear temperature dependence (T1^4 - T2^4).

Characteristics of Radiation

• Surfaces: Heat transfer through radiation doesn't require a medium (can occur in a vacuum).
• Practical Example: Feeling heat from a fire is due to radiation, not air temperature.
• Comparison to Light: Thermal radiation is part of the electromagnetic spectrum, similar to visible light.

Stefan-Boltzmann Law

• Formula: Emissive power (E) = εσT^4
  • ε: Emissivity of the surface (0 to 1).
  • σ: Stefan-Boltzmann constant (5.67 × 10^-8 W/m²K⁴).
  • T: Absolute temperature of the surface in Kelvin.
• Emissivity (ε): Ratio of heat emitted by a surface compared to a black body.
  • Black body: Perfect emitter with ε = 1.

Surface Phenomenon

• Any measurable temperature surface emits radiative energy.

• View Factor: Determines how much radiation moves from one surface to another.

• Radiative Heat Flux: Net flow of radiation from a surface calculated using:

  [ q_{rad}'' = εσ(T_s^4 - T_{surroundings}^4) ]

• Gray Surface Assumption: Assumes absorptivity = emissivity.

Application Example

• Problem: Calculate the heat loss from a roof by radiation.
  • Parameters: Roof temperature = 35°C, Surroundings temperature = 20°C, Surface area = 50 m², ε = 0.85.
  • Calculation Steps:
    • Convert temperatures to Kelvin.
    • Use Stefan-Boltzmann Law to calculate the radiative heat flux.
    • Multiply by surface area for total heat loss.
  • Result: Roof loses approximately 3,926 Watts by radiation.

Important Concepts

• Temperature: Radiation increases significantly at high temperatures.
• Concurrent Heat Transfer: Radiation and convection can occur simultaneously.
• Practical Impact: Radiation becomes dominant at high temperatures (e.g., feeling heat from a fire).

Simplified Stefan-Boltzmann Law for Practice

• Remember this equation for small objects exchanging heat with surroundings:

  [ q_{rad}'' = εσ(T_1^4 - T_2^4) ]

• Usage: Apply when assuming uniform temperature surroundings and small object size relative to surroundings.

Closing

• The lecture emphasizes understanding the basics of radiation and applying the Stefan-Boltzmann Law to simple problems. More complex geometries and conditions will be covered in future chapters.