Table of Contents
Conduction, Convection and Thermal Radiation
1. Introduction
Heat transfer is the movement of thermal energy from one region or body to another because of a temperature difference. It occurs in homes, industries, power stations, vehicles, oceans and the Earth’s atmosphere.
There are three principal mechanisms of heat transfer:
- Conduction
- Convection
- Thermal radiation
These mechanisms may operate separately or simultaneously. For example, when water is heated in a metal saucepan, heat travels through the metal by conduction, circulates through the water by convection, and is also transferred from the hot surface to its surroundings by radiation.
Understanding heat transfer is essential in building design, refrigeration, cooking, climate science, power generation and engineering.
2. Conduction
Conduction is the transfer of thermal energy through a substance or between bodies in contact without bulk movement of the material itself.
It is particularly important in solids.
When one end of a metal rod is heated, particles in the hotter region vibrate more energetically. They transfer energy to neighbouring particles through interactions. In metals, mobile electrons also contribute significantly to heat conduction.
2.1 Mechanism of Conduction
Conduction occurs through microscopic interactions within a material.
- In solids, atoms and molecules transfer energy through vibrations and interactions.
- In metals, free electrons carry energy rapidly through the material.
- In liquids and gases, conduction occurs through molecular collisions and interactions, although convection may also occur.
2.2 Thermal Conductors
Materials that allow heat to pass through them relatively easily are called thermal conductors.
Examples include:
- Copper
- Aluminium
- Silver
- Iron
- Steel
Metals are generally good thermal conductors because of their mobile electrons.
2.3 Thermal Insulators
Materials that resist the transfer of heat are called thermal insulators.
Examples include:
- Wood
- Rubber
- Plastic
- Fibreglass
- Mineral wool
- Air trapped in insulating materials
Air is a relatively poor conductor of heat when it is stationary. However, moving air can transfer heat by convection.
3. Fourier’s Law of Heat Conduction
Fourier’s law describes the rate of heat conduction through a material.
For a uniform plane slab under steady-state conditions:
[
\frac{Q}{t}=\frac{kA(T_1-T_2)}{L}
]
Where:
- (Q) = heat transferred
- (t) = time
- (k) = thermal conductivity
- (A) = cross-sectional area
- (T_1-T_2) = temperature difference across the material
- (L) = thickness or length of the material
The SI unit of thermal conductivity is:
[
\text{W m}^{-1}\text{K}^{-1}
]
The equation shows that the rate of conduction increases with thermal conductivity, area and temperature difference. It decreases as the thickness of the material increases.
3.1 Thermal Conductivity
Thermal conductivity is a measure of a material’s ability to conduct heat.
A material with high thermal conductivity transfers heat more readily than a material with low thermal conductivity under comparable conditions.
For example, copper has a much higher thermal conductivity than wood.
3.2 Factors Affecting Conduction
The rate of heat conduction depends on:
- Thermal conductivity of the material.
- Cross-sectional area.
- Temperature difference.
- Thickness of the material.
- Duration of heat transfer.
4. Applications of Conduction
4.1 Cooking Utensils
Metal cooking pots and pans conduct heat from a stove to food.
Copper and aluminium are used in cookware because of their relatively high thermal conductivity.
4.2 Building Insulation
Walls and roofs use insulating materials to reduce heat transfer between indoor and outdoor environments.
4.3 Heat Sinks
Electronic devices generate heat during operation. Heat sinks, commonly made of aluminium or copper, conduct heat away from electronic components.
4.4 Thermal Clothing
Clothing traps layers of relatively stationary air, reducing heat loss from the body.
4.5 Industrial Furnaces
Refractory materials are used to resist heat transfer and protect industrial furnace structures.
5. Convection
Convection is the transfer of thermal energy through the bulk movement of a fluid.
It occurs in liquids and gases because their particles can move from one location to another.
When a fluid is heated, it generally expands and becomes less dense. The warmer, less dense fluid tends to rise, while cooler, denser fluid tends to move downward.
This movement produces convection currents.
5.1 Natural Convection
Natural convection occurs because of density differences produced by temperature variations, without an external mechanical device forcing the fluid to move.
Examples include:
- Warm air rising above a heater.
- Circulation of water in a heated pot.
- Sea breezes.
- Atmospheric circulation.
5.2 Forced Convection
Forced convection occurs when fluid movement is produced by an external device such as a fan, pump or blower.
Examples include:
- Fans circulating air in rooms.
- Water pumps in engine cooling systems.
- Airflow through radiators.
- Forced-air heating systems.
6. Convection Currents
A convection current is a circulating movement of fluid caused by temperature-related density differences.
Consider water being heated in a container:
- Water near the heat source becomes warmer.
- Its density generally decreases.
- Warmer water rises.
- Cooler, denser water moves downward.
- The cycle continues, distributing heat throughout the liquid.
Convection currents are responsible for the circulation of heat in many natural and engineered systems.
7. Newton’s Law of Cooling
Newton’s law of cooling describes the rate at which an object loses heat to its surroundings.
For relatively small temperature differences and approximately constant surrounding conditions, the rate of cooling is approximately proportional to the temperature difference between the object and its surroundings.
[
\frac{dT}{dt}=-k(T-T_s)
]
Where:
- (T) = temperature of the object
- (T_s) = surrounding temperature
- (t) = time
- (k) = cooling constant, dependent on the system
The negative sign indicates that the object’s temperature decreases when it is hotter than its surroundings.
Newton’s law of cooling is an approximation. It is most useful when the temperature difference is not extremely large and the heat-transfer conditions remain reasonably stable.
7.1 Applications
- Estimating the cooling time of hot liquids.
- Studying cooling of manufactured products.
- Food cooling and storage.
- Forensic estimation of time since death, subject to many environmental uncertainties.
- Designing cooling equipment.
8. Thermal Radiation
Thermal radiation is the transfer of energy through electromagnetic waves emitted by matter because of its temperature.
Unlike conduction and convection, radiation does not require a material medium.
It can occur through a vacuum.
The Sun transfers energy to Earth through electromagnetic radiation across space.
8.1 Characteristics of Thermal Radiation
- All objects above absolute zero emit thermal radiation.
- Radiation can travel through a vacuum.
- Hotter objects generally emit more radiation.
- The spectrum of radiation depends on temperature.
- Dark, matte surfaces generally absorb and emit thermal radiation more effectively than highly reflective surfaces.
9. Blackbody Radiation
A blackbody is an ideal physical object that absorbs all incident electromagnetic radiation, regardless of wavelength or direction.
It is also an ideal emitter of radiation at a given temperature.
A perfect blackbody is a theoretical model, but some physical systems approximate its behaviour.
Blackbody radiation is important in understanding stars, thermal emission, temperature measurement and quantum physics.
9.1 Absorption and Emission
A surface that absorbs radiation efficiently is generally also an efficient emitter at the same wavelength and under the same thermodynamic conditions.
A polished silver surface is a relatively poor absorber and emitter of thermal radiation compared with a black, matte surface.
10. Stefan-Boltzmann Law
The Stefan-Boltzmann law states that the total radiant energy emitted per unit area of a perfect blackbody per unit time is proportional to the fourth power of its absolute temperature.
[
E=\sigma T^4
]
Where:
- (E) = radiant power emitted per unit area
- (\sigma) = Stefan-Boltzmann constant
- (T) = absolute temperature in kelvin
The Stefan-Boltzmann constant is:
[
\sigma=5.670374419\times10^{-8}\
\text{W m}^{-2}\text{K}^{-4}
]
For a real surface with emissivity (\varepsilon):
[
P=\varepsilon\sigma AT^4
]
Where:
- (P) = total emitted radiant power
- (\varepsilon) = emissivity
- (A) = surface area
For an object exchanging radiation with large surroundings at temperature (T_s), the net radiative heat-transfer rate can be approximated by:
[
P_{\text{net}}=\varepsilon\sigma A(T^4-T_s^4)
]
This expression assumes an appropriate simplified radiative environment and a surface whose emissivity can be treated as constant.
11. Wien’s Displacement Law
Wien’s displacement law relates the temperature of a blackbody to the wavelength at which its emission is strongest.
[
\lambda_{\max}T=b
]
Where:
- (\lambda_{\max}) = wavelength of maximum emission
- (T) = absolute temperature
- (b) = Wien’s displacement constant
[
b\approx2.898\times10^{-3}\ \text{m K}
]
As temperature increases, the wavelength of maximum emission decreases.
This explains why very hot objects can glow with different visible colours and why stars of different surface temperatures have different characteristic colours.
12. Emissivity
Emissivity is the ratio of radiation emitted by a real surface to that emitted by an ideal blackbody at the same temperature and under comparable conditions.
It is represented by (\varepsilon).
For an ideal blackbody:
[
\varepsilon=1
]
For ordinary real surfaces:
[
0\leq\varepsilon\leq1
]
Emissivity depends on the material, surface condition and wavelength.
13. Kirchhoff’s Law of Thermal Radiation
Kirchhoff’s law states that, under thermal equilibrium and at a specified wavelength, the emissivity of a surface equals its absorptivity.
In simplified terms, a good absorber is also a good emitter under corresponding conditions.
This principle helps explain why:
- Dark, matte surfaces are effective absorbers and emitters.
- Polished reflective surfaces are relatively poor absorbers and emitters.
14. Comparison of the Three Methods of Heat Transfer
| Feature | Conduction | Convection | Radiation |
|---|---|---|---|
| Main mechanism | Microscopic interactions and collisions | Bulk fluid movement | Electromagnetic waves |
| Requires matter? | Yes | Yes | No |
| Occurs in solids? | Yes | Not as bulk convection | Yes |
| Occurs in liquids and gases? | Yes | Yes | Yes |
| Can occur through vacuum? | No | No | Yes |
| Example | Metal spoon heating | Warm air rising | Sun heating Earth |
15. Combined Heat Transfer in Everyday Life
Several heat-transfer mechanisms commonly operate together.
15.1 Cooking on a Stove
- The stove heats the pan through conduction.
- The pan transfers heat to food by conduction.
- Water or oil inside the pan circulates through convection.
- The flame and hot surfaces also transfer energy through radiation.
15.2 Heating a Room
- A radiator transfers heat to nearby air through conduction and convection.
- Warm air circulates around the room.
- The radiator also emits thermal radiation.
15.3 Cooling an Automobile Engine
- Coolant absorbs heat from the engine through conduction across surfaces.
- The coolant transports energy through convection.
- The radiator transfers heat to the surrounding air, assisted by forced airflow from a fan.
16. Worked Examples
Example 1: Heat Conduction Through a Wall
A wall has a thermal conductivity of (0.8\ \text{W m}^{-1}\text{K}^{-1}), an area of 10 m² and a thickness of 0.2 m. The temperature difference across it is 15 K. Calculate the steady rate of heat transfer.
Using:
[
\frac{Q}{t}=\frac{kA\Delta T}{L}
]
Substituting:
[
\frac{Q}{t}=\frac{0.8\times10\times15}{0.2}
]
[
\boxed{\frac{Q}{t}=600\ \text{W}}
]
The wall transfers heat at an approximate rate of 600 W under the stated steady-state assumptions.
Example 2: Radiation from a Blackbody
A blackbody has a surface temperature of 500 K. Calculate the radiant power emitted per square metre.
Using:
[
E=\sigma T^4
]
[
E=5.67\times10^{-8}\times500^4
]
[
E=5.67\times10^{-8}\times6.25\times10^{10}
]
[
\boxed{E\approx3544\ \text{W m}^{-2}}
]
Example 3: Wien’s Law
Calculate the wavelength of maximum emission for a blackbody at 5800 K.
Using:
[
\lambda_{\max}=\frac{b}{T}
]
[
\lambda_{\max}=\frac{2.898\times10^{-3}}{5800}
]
[
\boxed{\lambda_{\max}\approx5.0\times10^{-7}\ \text{m}}
]
This is approximately 500 nm, within the visible region of the electromagnetic spectrum.
17. Practical Importance
Heat-transfer principles are used in:
- Building insulation and energy-efficient architecture.
- Refrigeration and air conditioning.
- Power generation.
- Automobile cooling systems.
- Cooking and food processing.
- Solar energy systems.
- Weather and climate science.
- Industrial furnaces.
- Electronic equipment cooling.
- Medical thermal devices.
36 Key Takeaways for Exams
- Heat transfer is the movement of thermal energy due to a temperature difference.
- The three principal modes of heat transfer are conduction, convection and radiation.
- Conduction transfers heat without bulk movement of matter.
- Conduction is particularly important in solids.
- Metals are generally good thermal conductors.
- Mobile electrons contribute significantly to heat conduction in metals.
- Thermal insulators resist the transfer of heat.
- Thermal conductivity measures a material’s ability to conduct heat.
- The SI unit of thermal conductivity is W m(^{-1}) K(^{-1}).
- Fourier’s law describes heat conduction.
- A greater temperature difference generally increases the rate of conduction.
- A thicker material generally reduces the rate of heat conduction.
- Convection involves the bulk movement of fluids.
- Convection occurs in liquids and gases.
- Natural convection is driven by temperature-related density differences.
- Forced convection uses an external device such as a fan or pump.
- Warm fluid generally rises because it is less dense than cooler fluid.
- Convection currents distribute heat within fluids.
- Newton’s law of cooling relates cooling rate to the temperature difference between an object and its surroundings.
- Newton’s law of cooling is an approximation under specified conditions.
- Thermal radiation transfers energy through electromagnetic waves.
- Radiation does not require a material medium.
- The Sun transfers energy to Earth through radiation.
- A blackbody is an ideal absorber and emitter of radiation.
- The Stefan-Boltzmann law relates blackbody emission to the fourth power of absolute temperature.
- The Stefan-Boltzmann constant is approximately (5.67\times10^{-8}) W m(^{-2}) K(^{-4}).
- Emissivity measures the emission of a real surface relative to a blackbody.
- The emissivity of an ideal blackbody is 1.
- Wien’s displacement law relates peak emission wavelength to absolute temperature.
- Higher blackbody temperature corresponds to a shorter peak wavelength.
- Kirchhoff’s law relates emissivity and absorptivity under thermal equilibrium conditions.
- Dark, matte surfaces are generally good absorbers and emitters of thermal radiation.
- Polished reflective surfaces are generally poor absorbers and emitters.
- Cooking commonly involves conduction, convection and radiation together.
- Heat sinks transfer thermal energy away from electronic components.
- Heat-transfer principles are essential in engineering, building design, refrigeration and climate science.