Heat transfer Chapter 4: Radiative heat transfer

This chapter introduces radiative heat transfer as energy transport by electromagnetic radiation. Unlike conduction and convection, radiation does not require a material medium and becomes dominant at high temperatures or when other mechanisms are weak. These notes explain the physical nature of radiation, its interaction with media and surfaces, the concept of directionality and spectra, and how radiation is modeled in CFD using surface-based and volumetric approaches. Emphasis is placed on regime identification, simplifying assumptions, and practical model selection

---

Why Radiation Is Fundamentally Different

Radiation differs from conduction and convection in three essential ways:

1. No medium is required
   Radiation propagates through vacuum, unlike conduction and convection, which require matter.

2. Strong temperature dependence
   Radiative emission increases extremely rapidly with temperature, making radiation dominant in high-temperature systems.

3. Directional and spectral nature
   Radiation travels along specific directions and spans a wide range of wavelengths.

Because of these features, radiation often:

• Competes with conduction and convection at high temperatures

• Dominates heat transfer in space, furnaces, combustion, and solar-driven systems

• Requires fundamentally different modeling tools

---

Physical Nature of Radiation

3.1 Wave–Particle Duality

Radiation can be described from two complementary perspectives:

• Wave perspective
  Radiation is an electromagnetic wave governed by Maxwell’s equations. This view explains:

  • Propagation

  • Reflection

  • Refraction

  • Polarization

• Particle (quantum) perspective
  Radiation consists of photons carrying discrete packets of energy. This view explains:

  • Emission

  • Absorption

  • Spectral behavior

Radiative heat transfer relies on both perspectives:

• Wave view → transport through space and media

• Particle view → emission and absorption mechanisms

3.2 Thermal Radiation

Thermal radiation is emitted by all matter above absolute zero due solely to temperature.

Key characteristics:

• Lies mainly in the infrared range

• Spectrum and intensity depend on temperature

• Hotter objects emit:

  • More radiation

  • At shorter wavelengths

This explains:

• Incandescence of hot metals

• Infrared dominance of room-temperature radiation

• Solar radiation spectrum reaching Earth

---

4. Radiation as a Directional Quantity

4.1 Direction of Propagation

Radiation at a point does not arrive uniformly from all directions. Instead:

• Each ray travels along a specific direction

• Intensity depends on direction

To describe this:

• Directions are mapped onto a unit sphere

• Each direction corresponds to a point on the sphere

4.2 Solid Angle

The solid angle quantifies how much of the directional space is occupied.

Physical meaning:

• Measures how “large” an object appears from a point

• Independent of actual size; depends on distance and orientation

Why this matters:

• Radiative exchange depends on geometry

• Directional integration is central to radiation models

---

Radiative Quantities (Physical Meaning)

Key quantities used in radiation modeling:

• Radiation intensity
  Energy carried in a given direction per unit area and solid angle.

• Irradiation
  Total radiation incident on a surface from all directions.

• Emissive power
  Radiation emitted by a surface or medium.

• Radiative heat flux
  Net radiative energy crossing a surface.

Important distinction:

• Unlike conduction and convection, radiation is inherently non-local: surfaces exchange energy across space.

---

Interaction of Radiation with Media

6.1 Participating vs Non-Participating Media

• Non-participating media

  • Transparent to radiation

  • Do not absorb, emit, or scatter

  • Radiation interacts only with surfaces

• Participating media

  • Absorb, emit, and possibly scatter radiation

  • Radiation becomes a volumetric phenomenon

Examples:

• Air at room temperature → weakly participating

• Combustion gases, soot, glass → participating

6.2 Absorption and Emission

Absorption:

• Radiation energy is converted into internal energy of the medium

Emission:

• Medium releases radiation based on its temperature

Under local thermodynamic equilibrium (LTE):

• Emission depends only on local temperature

• This assumption is valid for most engineering flows

6.3 Scattering

Scattering redistributes radiation direction without necessarily changing energy.

Important cases:

• Particles, droplets, aerosols

• Atmosphere (sky radiation)

In many engineering applications:

• Scattering is neglected to simplify modeling

• Valid when particles are small or sparse

---

Radiative Transfer Equation (Conceptual)

The radiative transfer equation (RTE) balances, along a ray:

• Loss by absorption

• Gain by emission

• Redistribution by scattering

• Transport along direction

Why it is challenging:

• Depends on space, direction, wavelength, and time

• High dimensionality makes exact solutions impractical

All radiation models are approximations to the RTE.

---

Radiation at Surfaces

8.1 Surface Properties

Surfaces interact with radiation through:

• Absorptivity: fraction absorbed

• Reflectivity: fraction reflected

• Transmissivity: fraction transmitted

For opaque surfaces:

• Transmissivity is zero

• Absorption + reflection = 1

8.2 Emissivity and Kirchhoff’s Law

Emissivity measures how efficiently a surface emits radiation compared to an ideal emitter.

Kirchhoff’s law states:

• At equilibrium, emissivity equals absorptivity

This links:

• How well a surface emits

• How well it absorbs incoming radiation

8.3 Diffuse vs Specular Surfaces

• Diffuse surfaces
  Radiation is reflected/emitted uniformly in all directions

• Specular surfaces
  Reflection follows mirror-like behavior

Most engineering radiation models assume diffuse-gray surfaces for tractability.

---

Optical Thickness and Regimes

9.1 Optical Thickness

Optical thickness measures how strongly a medium interacts with radiation over a characteristic length.

Interpretation:

• Optically thin → radiation passes through largely unaffected

• Optically thick → radiation is absorbed and re-emitted many times

This single concept determines:

• Whether radiation is surface-dominated or volumetric

• Which CFD radiation model is appropriate

---

Radiation Models in CFD (Fluent Perspective)

10.1 Surface-to-Surface (S2S)

• For non-participating media

• Radiation exchange only between surfaces

• Uses view factors to capture geometry

Advantages:

• Accurate for enclosures

• Low computational cost

Limitations:

• Cannot model gas radiation

10.2 Discrete Ordinates (DO)

• Solves RTE along discrete directions

• Handles participating media

• Captures shadowing and directional effects

Advantages:

• General-purpose

• Works with combustion and semi-transparent media

Limitations:

• Computationally expensive

• Requires angular resolution tuning

10.3 P-1 and Rosseland Models

• Diffusion-type approximations

• Best for optically thick media

Advantages:

• Very efficient

• Robust convergence

Limitations:

• Poor for optically thin or highly directional radiation

10.4 Monte Carlo

• Tracks photon bundles statistically

• Very high fidelity

Limitations:

• Extremely expensive

• Rarely used for routine CFD

---

Solar Load Model

11.1 Purpose

The Solar Load Model (SLM):

• Adds radiation from the Sun as an external source

• Is not a standalone radiation model

• Must be coupled with DO for internal radiation

11.2 Modeling Philosophy

Two approaches:

• Solar ray tracing: tracks collimated solar beams

• DO irradiation: integrates solar input into DO framework

Key features:

• Uses geographic location, date, and time

• Accounts for direct and diffuse solar radiation

• Ideal for HVAC, buildings, and automotive cabins

11.3 Limitations

• No internal re-radiation unless DO is active

• Simplified reflection and scattering

• Single dominant solar direction

Despite this, SLM is:

• Efficient

• Easy to use

• Highly practical for climate simulations

---

Physical Interpretation and Engineering Intuition

• Radiation dominates at high temperature or low convection

• Geometry strongly controls radiative exchange

• Emissivity matters more than conductivity at high temperatures

• Optical thickness determines whether gas radiation matters

• Radiation models trade accuracy for computational cost

Rule of thumb:

If you can “see” a hot surface, radiation is likely important.

---

Study Priorities

If time is limited, the most important concepts to look into:

1. Why radiation differs from conduction and convection

2. Thermal radiation and temperature dependence

3. Participating vs non-participating media

4. Optical thickness concept

5. Surface properties and emissivity

6. Choosing the right CFD radiation model

---

Key Takeaways

• Radiation transfers energy via electromagnetic waves.

• It does not require a medium and is strongly temperature-dependent.

• Directionality and spectra make radiation complex.

• Optical thickness governs modeling strategy.

• CFD radiation models are approximations to the RTE.

• Solar loading is a special but important engineering case