Explain some of the complex applications and consequences of conduction, convection and radiation where more than one type of thermal energy transfer is significant, including: (a) a fire burning wood or coal (b) a radiator in a car

2.3.4 Consequences of Thermal Energy Transfer

In most real‑world systems more than one mode of heat transfer operates simultaneously. Understanding how conduction, convection and radiation interact enables us to predict the behaviour of everyday devices, to design efficient equipment and to apply the correct safety measures.

Key Concepts

• Conduction – transfer of kinetic energy through direct collisions of neighbouring particles.

  • Most efficient in solids because particles are close together.
  • In liquids the particles are farther apart, so the thermal conductivity is lower.
  • Gases have the lowest conductivity – the large mean free path means collisions are infrequent.
  • In metals the dominant carriers are free electrons (phonon + electron conduction); in insulators heat is carried by lattice vibrations (phonons).

• Convection – heat carried by the bulk movement of a fluid (liquid or gas).

  • Natural (buoyancy‑driven) – hot fluid becomes less dense, rises, and cooler fluid sinks.
  • Forced – a pump, fan or the motion of a vehicle forces the fluid to move.
  • Quantitatively, the heat flow is
    

    \(Q_{\text{conv}} = h\,A\,\Delta T\)

    where \(h\) is the convective heat‑transfer coefficient (W m⁻² K⁻¹).

  • Natural convection starts when the Rayleigh number \(Ra\) exceeds a critical value (≈ 10³–10⁴); this links temperature difference, fluid properties and characteristic length.

• Radiation – emission of electromagnetic waves (mainly infrared) from any body whose temperature is above absolute zero.

  • No material medium is required.
  • For a grey surface (emissivity \(\varepsilon\) roughly constant over the relevant wavelengths) the net radiative power is

    \(P{\text{rad}} = \varepsilon \,\sigma \,A\,(T^{4}-T{\text{amb}}^{4})\)

    with \(\sigma = 5.67\times10^{-8}\ \text{W m}^{-2}\text{K}^{-4}\).

  • Colour and surface texture affect \(\varepsilon\):

    • Black or matte surfaces have high emissivity (\(\varepsilon\approx0.9\)) and absorb/emit strongly.
    • Polished metal reflects infrared and has a low \(\varepsilon\) (≈ 0.05–0.1).
    • Roughness increases the effective surface area, raising both emissivity and convective area.

Interaction of the Three Modes

Heat is often first conducted from a hot interior to a surface, then removed from that surface by convection and/or radiation. The dominant mode depends on temperature, geometry and the surrounding medium.

Everyday Examples (beyond the kettle)

• Domestic wall radiator – conduction from hot water to the metal panel, natural convection of room air, and a small radiative contribution.
• Toaster – conduction through the metal heating element, convection of surrounding air, and radiation that browns the bread.
• Hair‑dryer – forced convection of air heated by a resistive element (conduction), with a noticeable infrared glow (radiation).

Case Study (a): A Fire Burning Wood or Coal

Energy‑flow diagram (suggested)

Insert a cross‑section diagram showing: hot glowing embers, rising hot gases, and infrared rays reaching surrounding objects.

Processes and interaction of modes

1. Combustion (chemical reaction) releases thermal energy \(Q\).
2. Conduction transfers heat from the hot core of an ember into adjacent un‑burnt wood, raising its temperature to the ignition point.
3. Convection – hot gases expand, become less dense and rise. This creates a continuous flow that:

   • supplies fresh oxygen to the flame,
   • carries combustion products away, and
   • transports heat away from the flame.

4. Radiation – the flame and glowing embers emit infrared radiation that heats objects not in direct contact (e.g., a pot placed nearby).

Why radiation dominates at high temperature

Radiative power varies as \(T^{4}\). When the temperature exceeds about 600 K the \(T^{4}\) term grows much faster than the linear dependence of conduction or convection on \(\Delta T\), so most of the heat loss from a fire is by radiation.

Simple quantitative examples

• Conduction (Fourier’s law) – heat flow through a wooden plank of length \(L=0.05\ \text{m}\) and area \(A=0.01\ \text{m}^2\):

  
  \(Q_{\text{cond}} = k\,A\,\frac{\Delta T}{L}\)

  with wood thermal conductivity \(k\approx0.12\ \text{W m}^{-1}\text{K}^{-1}\) and \(\Delta T = 300\ \text{K}\) gives

  \(Q_{\text{cond}} \approx 7\ \text{W}\). This is small compared with the radiative output of the same ember.

• Convection estimate – for air flowing over the radiator (forced convection) with \(h\approx40\ \text{W m}^{-2}\text{K}^{-1}\), area \(A=1.2\ \text{m}^2\) and \(\Delta T = 80\ \text{K}\):

  
  \(Q_{\text{conv}} = h A \Delta T \approx 40 \times 1.2 \times 80 \approx 3.8\times10^{3}\ \text{W}\)

  showing why forced convection is the principal cooling mechanism in a moving car.

• Radiation from an ember (as in the original notes):

  
  \(P_{\text{rad}} = 0.9 \times 5.67\times10^{-8} \times 0.02 \times (800)^{4} \approx 2.3\times10^{3}\ \text{W}\)

Consequences

• Rapid spread of fire because conduction ignites the next piece of fuel while convection distributes hot gases.
• High‑temperature flames are efficient radiators; a small increase in temperature yields a large increase in radiative loss.
• In enclosed spaces convection can trap hot, poisonous gases (CO, smoke).
• Fire‑fighting strategies target specific modes:

  • Water – absorbs heat (conduction) and cools the fire.
  • Fire blanket – blocks radiation and limits oxygen supply.
  • Ventilation control – reduces the convective supply of fresh air.

Simple convection experiment (satisfying the syllabus)

1. Fill a tall, clear glass tube with water.
2. Add a few drops of food colouring at the bottom.
3. Heat the bottom of the tube gently (e.g., with a lamp).
4. Observe the coloured water rise as it warms – a visual demonstration of natural convection driven by density differences.

Safety & practical precautions

• Keep flammable materials away from the flame – conduction can ignite them before they touch the fire.
• Use fire blankets or sand to cut off radiation and oxygen.
• Provide adequate ventilation to avoid buildup of hot, toxic gases produced by convection.
• Never use water on a grease fire – rapid steam formation creates violent convection currents.

Case Study (b): A Radiator in a Car

Energy‑flow diagram (suggested)

Insert a schematic showing: engine block → coolant → radiator tubes → air flow (fan or vehicle motion) → ambient air.

Processes and interaction of modes

1. Conduction – heat generated in the engine block is conducted to the coolant flowing through narrow passages.
2. Forced convection – the water pump circulates hot coolant through the radiator; a fan (or the car’s motion) forces air over the finned tubes, removing heat.
3. Natural convection – when the vehicle is stationary, buoyancy‑driven air movement around the radiator still carries away some heat.
4. Radiation – the hot aluminium tubes emit infrared radiation; this contribution is small but becomes noticeable at high surface temperatures.

Key definitions

• Convective heat‑transfer coefficient \(h\) – a measure of how efficiently a fluid removes heat from a surface (W m⁻² K⁻¹). Typical values:

  • Forced air over a radiator: \(h \approx 30\!-\!50\ \text{W m}^{-2}\text{K}^{-1}\).
  • Natural air flow: \(h \approx 5\!-\!10\ \text{W m}^{-2}\text{K}^{-1}\).

• Emissivity \(\varepsilon\) of a painted aluminium radiator ≈ 0.85–0.95 (high, because the paint is usually black‑grey).

Quantitative illustration (radiative loss)

Assume total radiating area \(A = 1.2\ \text{m}^2\), surface temperature \(T{\!s}=380\ \text{K}\), ambient temperature \(T{\!amb}=300\ \text{K}\), \(\varepsilon = 0.9\).

\(P{\text{rad}} = \varepsilon \sigma A\bigl(T{\!s}^{4}-T_{\!amb}^{4}\bigr)

\approx 0.9 \times 5.67\times10^{-8} \times 1.2 \times (380^{4}-300^{4})

\approx 4.5\times10^{2}\ \text{W}\)

Typical convective removal is several kilowatts, so radiation accounts for roughly 5 % of the total heat loss at normal operating conditions.

Consequences

• Temperature difference – efficient cooling requires a large \(\Delta T = T{\text{coolant}}-T{\text{air}}\); the convective heat loss \(Q = h A \Delta T\) scales directly with this difference.
• Stopped vehicle – forced convection drops dramatically; natural convection and radiation become relatively more important. If the fan fails, the engine can overheat quickly.
• Thermal expansion – conduction heats metal parts, causing expansion that can stress gaskets and lead to leaks.
• Insufficient coolant flow – creates local hot spots, increasing the risk of engine knock or pre‑ignition.

Safety & practical precautions (car)

• Check coolant level regularly – low coolant reduces conductive heat transfer from the engine.
• Ensure the radiator fan operates correctly; a failed fan eliminates forced convection.
• Keep the radiator fins clean – dirt reduces the effective surface area for both convection and radiation.
• Never open the radiator cap when the engine is hot – rapid steam release can cause severe burns (latent heat transferred by conduction).

Dominant‑Mode Summary (quick revision)

Summary of Interactions

• In a fire, heat is first conducted into fresh fuel, convection spreads hot gases and supplies oxygen, and radiation carries the bulk of the energy away as infrared light.
• In a car cooling system, conduction moves engine heat to the coolant, forced convection removes most of that heat via airflow, while natural convection and radiation act as safety nets when airflow is limited.
• Design improvements (fin geometry, coolant flow rate, fan control, emissive coatings) aim to optimise the balance between the three modes for efficiency, reliability and safety.

Alignment with Cambridge IGCSE 0625 Syllabus (Section 2.3.4)