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Thermodynamics tells you how much heat must move; heat transfer tells you how fast it moves and what temperatures result. It decides the size of a heat sink, the thickness of insulation on an oven, whether a motor overheats and how hot an exhaust manifold’s surface gets. Heat moves in three ways: conduction, convection and radiation.
Conduction
Heat flows through a solid (or a still fluid) from hot to cold, passed from molecule to molecule. Fourier’s law gives the rate through a flat wall:
| Symbol | Meaning | Unit |
|---|---|---|
| Heat flow rate | W | |
| Thermal conductivity of the material | W/m·K | |
| Area the heat flows through | m² | |
| Temperature difference across the wall | K | |
| Wall thickness | m |
| Material | k (W/m·K, approx.) |
|---|---|
| Copper | 400 |
| Aluminium | 200–240 |
| Carbon steel | 50 |
| Stainless steel | 15 |
| Glass | 1 |
| Water | 0.6 |
| Wood | 0.1–0.2 |
| Mineral wool insulation | 0.04 |
| Still air | 0.026 |
Convection
Heat is carried between a surface and a moving fluid. Natural convection happens when warm fluid rises by itself; forced convection uses a fan or pump. Newton’s law of cooling gives the rate:
| Symbol | Meaning | Unit |
|---|---|---|
| Convection heat transfer coefficient | W/m²·K | |
| Surface temperature | K | |
| Fluid temperature away from the surface | K |
The coefficient depends on the fluid, its speed and the geometry, and it is found from experiments and correlations.
| Situation | h (W/m²·K, typical range) |
|---|---|
| Natural convection, gases | 2–25 |
| Forced convection, gases | 25–250 |
| Natural convection, liquids | 50–1000 |
| Forced convection, liquids | 100–20 000 |
| Boiling and condensation | 2500–100 000 |
Radiation
Every surface above absolute zero gives off electromagnetic radiation, and it needs no medium: it crosses a vacuum. The net exchange between a small surface and large surroundings is:
where is the surface emissivity (0 to 1: about 0.05 for polished aluminium, 0.8–0.95 for painted or oxidised surfaces), W/m²·K⁴ is the Stefan–Boltzmann constant, and the temperatures are absolute. Because of the fourth power, radiation dominates at high temperatures: in furnaces, around exhausts and near flames.
Thermal resistance: adding up a wall
Heat flowing through layers in series behaves like current through resistors in series. Each layer and each surface has a resistance, and they simply add:
The layer with the largest resistance takes most of the temperature drop, which is exactly what insulation is for.
Assumptions
- Steady state: temperatures don’t change with time.
- One-dimensional heat flow through a flat wall, with no heat generated inside it.
- Constant thermal conductivity and constant convection coefficients.
- Radiation ignored in the wall problem below (it would add a parallel path at the hot surface).
Solved problem: an insulated oven wall
An oven wall is 5 mm steel (k = 50 W/m·K) with 50 mm of mineral wool outside it (k = 0.04 W/m·K). The gas inside is at 300 °C with h = 20 W/m²·K; the room is at 25 °C with h = 10 W/m²·K. Find the heat loss per square metre and the temperature of the outer surface. Then compare with no insulation.
Step 1: resistances for 1 m² of wall.
(all in K/W for 1 m²)
Step 2: total resistance and heat flow.
Step 3: outer surface temperature. The heat crosses the outer air film:
Step 4: without insulation.
The insulation carries almost 90 % of the total resistance, so it takes almost all the temperature drop. The steel layer is so conductive that it hardly matters.
Solved problem: radiation from a hot plate
A painted steel plate of 0.5 m² (ε = 0.8) is at 200 °C in a large room at 25 °C. Find the heat it loses by radiation.
Step 1: absolute temperatures. T_s = 473.15 K, T_sur = 298.15 K.
Step 2: apply the Stefan–Boltzmann law.
Where it matters in design
- Cooling: fins increase the area A to raise heat loss from motors, electronics and engine cylinders; a fan raises h.
- Insulation: low-k materials add a large resistance in ovens, cold rooms and exhaust heat shields.
- Thermal stress: uneven temperatures cause uneven expansion and stress, especially in castings and welded parts that heat up quickly.
- Material choice: aluminium spreads heat well for heat sinks; stainless steel conducts poorly, which is useful in handles and thermal breaks.
Key points
- Conduction: kAΔT/L. Convection: hAΔT. Radiation: εσA(T⁴ − T⁴), with absolute temperatures.
- Resistances in series add up; the largest resistance takes most of the temperature drop.
- Radiation grows with the fourth power of temperature and matters most for hot surfaces.
- Raise heat loss with area (fins) and h (fans); reduce it with low-k insulation.