Heat Transfer Modes: Radiation, Planck’s Law, and Convection Analysis
Radiation Heat Transfer Fundamentals
Radiation heat transfer is the transfer of thermal energy from a body in the form of electromagnetic waves (mainly infrared radiation).
It does not require any medium, so it can occur even in a vacuum. A common example is the heat reaching Earth from the Sun.
Radiation vs. Conduction and Convection
| Mode | Medium Required? | How Heat Transfers |
|---|---|---|
| Conduction | Yes (solid) | By direct molecular contact |
| Convection | Yes (fluid – liquid/gas) | By actual movement of fluid particles |
| Radiation | No medium required | By electromagnetic waves |
Thermal Radiation Shielding Techniques
Radiation shielding involves using materials or surfaces that block, reflect, or absorb thermal radiation to reduce heat transfer.
Minimizing Heat Transfer with Shields
- Using reflective surfaces (such as polished metals) reflects most of the incoming radiation.
- Using insulating coatings, ceramic layers, or multi-layer insulation reduces emitted radiation.
- Shields placed between the heat source and the object reduce the amount of radiation reaching the object.
Applications in High-Temperature Environments
- Furnace walls and insulation
- Spacecraft thermal protection systems
- High-temperature reactors
- Heat shields in engines and turbines
These shields help keep equipment cooler and improve overall efficiency.
Understanding Planck’s Law of Radiation
Planck’s Law states that:
A blackbody emits radiation at different wavelengths, and the intensity of radiation depends on both wavelength and the absolute temperature of the body.
Key Implications of Planck’s Law
- At any given temperature, radiation is spread over a range of wavelengths (forming a spectrum).
- As temperature increases, the total radiation intensity increases significantly, and the peak intensity shifts to shorter wavelengths.
Spectral Distribution and Temperature Dependence
Planck’s law provides the exact mathematical curve showing how radiation intensity varies with wavelength for a blackbody. It explains:
- Why hotter bodies emit substantially more energy.
- Why the color of hot objects changes (e.g., red shifts toward yellow and white) as temperature rises.
- How the peak emission wavelength depends inversely on temperature.
The Nusselt Number (Nu) in Convection
The Nusselt number (Nu) is a dimensionless number used to describe the enhancement of heat transfer in convection compared to pure conduction across the fluid layer.
Role of Nusselt Number in Forced Convection
- It indicates how effectively convection transfers heat from a surface to a moving fluid.
- A higher Nusselt number signifies more efficient convective heat transfer.
- It helps determine the strength of convective currents and is crucial in analyzing flow regimes (laminar or turbulent).
Relation to Heat Transfer Coefficient (h)
The Nusselt number is related to the convective heat transfer coefficient h by the following equation:
Nu = (h * L) / k
Where:
- h = convective heat transfer coefficient (W/m²·K)
- L = characteristic length (m)
- k = thermal conductivity of the fluid (W/m·K)
Rearranging this equation to solve for h:
h = (Nu * k) / L
Thus, as the Nusselt number increases, the heat transfer coefficient also increases, resulting in higher heat transfer rates in forced convection.
Impact of Surface Roughness on Heat Transfer
Increases Turbulence
Rough surfaces disturb the fluid flow and create significant turbulence near the wall.
Higher Heat Transfer Rate
Turbulence reduces the thickness of the thermal boundary layer, leading to better mixing and higher convective heat transfer.
Increase in Nusselt Number
Roughness increases Nu, which directly increases the heat transfer coefficient h.
Higher Friction Losses
Although heat transfer improves, rough surfaces also increase friction, leading to higher pumping power requirements and energy consumption.
Summary of Rough Surface Effects
- Rough surface → more turbulence → thinner boundary layer → higher heat transfer coefficient.
- However, this improvement comes at the cost of increased pressure drop and energy consumption.