Conduction
Conduction is the process by which thermal energy flows through a material — or between materials in direct contact — without any bulk movement of the material itself. When one end of a metal rod is held in a flame, the other end gradually becomes hot even though no part of the rod moves. That is conduction: energy is passed along through microscopic collisions between neighbouring atoms and free electrons, not by the material flowing from place to place. The driving force for conductive heat flow is always a temperature difference. Heat moves spontaneously from regions of higher temperature to regions of lower temperature, and it keeps flowing as long as that difference exists. The steeper the temperature gradient — that is, how rapidly temperature changes with distance — the faster energy is transported. This is why a thick wall insulates better than a thin one: a thicker barrier spreads the same temperature drop over a greater distance, reducing the gradient and slowing heat loss. Conduction matters enormously in everyday engineering and science. Building insulation, cooking pans, heat sinks in computers, and medical thermometers all rely on carefully chosen materials with specific conductive properties. Metals conduct heat well because their free electrons carry kinetic energy rapidly from atom to atom. Non-metals like wood, plastic, and air conduct poorly because they lack free electrons and rely on slower vibrational coupling between atoms. Understanding conduction quantitatively is the foundation of thermal engineering design.
- Thermal energy is kinetic energy of particles
- The role of free electrons in metals
- Temperature gradient as the driving force
- Thermal conductivity k as a material property
- Thermal resistance and series slabs
Thermal energy is kinetic energy of particles
Temperature is a measure of the average kinetic energy of the particles in a substance. Hotter regions contain particles vibrating or moving faster; cooler regions contain slower-moving particles. When particles in a hot region collide with neighbouring particles in a cooler region, they transfer some of their kinetic energy — the hot particles slow down slightly and the cool ones speed up. This is the microscopic engine driving conduction.
The role of free electrons in metals
Metals are exceptional conductors because they contain a 'sea' of free (delocalised) electrons that can travel through the lattice relatively unimpeded. When a metal is heated at one end, the energetic free electrons diffuse rapidly to cooler regions, delivering kinetic energy far faster than lattice vibrations alone could. This is why copper (thermal conductivity k ≈ 400 W m⁻¹ K⁻¹) conducts heat roughly 10,000 times better than glass (k ≈ 0.04 W m⁻¹ K⁻¹).
Temperature gradient as the driving force
The temperature gradient is defined as ΔT/Δx — the change in temperature per unit length along the direction of heat flow. Think of it like the slope of a hill: a steep slope (large gradient) causes a faster flow, while a gentle slope (small gradient) means slower flow. Doubling the temperature difference across a slab doubles the rate of heat transfer; doubling the thickness of the slab halves it. This linear relationship is captured precisely by Fourier's Law.
Thermal conductivity k as a material property
Different materials resist or facilitate heat flow to different degrees, characterised by thermal conductivity k, measured in watts per metre per kelvin (W m⁻¹ K⁻¹). A high k (e.g., silver, copper, aluminium) means heat flows easily. A low k (e.g., fibreglass, air, expanded polystyrene) means the material is a good insulator. Engineers choose materials with the appropriate k for their application — a frying pan needs high k for even heating, while a house wall needs low k to retain warmth.
Thermal resistance and series slabs
Just as electrical resistance limits current, thermal resistance R_th = L/(kA) limits heat flow. When multiple layers (e.g., a wall made of brick, insulation, and plasterboard) are stacked, their thermal resistances add in series, exactly like resistors in a series electrical circuit. The total resistance determines the overall heat flow rate for a given temperature difference. This analogy is extremely useful for analysing composite structures in building physics.
The Key Equation
- \dot{Q} — Rate of heat transfer (W (watts)): The amount of thermal energy transferred per unit time through the material.
- k — Thermal conductivity (W m⁻¹ K⁻¹): A material-specific constant expressing how readily the material conducts heat. Higher k means better conduction.
- A — Cross-sectional area (m²): The area of the slab perpendicular to the direction of heat flow. A larger area allows more heat to pass per second.
- \Delta T — Temperature difference (K or °C): The difference in temperature between the hot face and the cold face of the slab.
- L — Thickness (m): The length of the material in the direction of heat flow. Greater thickness reduces the rate of heat transfer.
Worked Example
Problem. A glass window pane is 4.0 mm thick and has an area of 1.5 m². On a cold day the inner surface is at 18 °C and the outer surface is at 2 °C. The thermal conductivity of glass is 0.96 W m⁻¹ K⁻¹. Calculate the rate at which heat is lost through the window by conduction.
Answer. The rate of heat loss through the window is 5760 W (5.76 kW).
Origins · 1 minJoseph Fourier and how this was discovered
Jean-Baptiste Joseph Fourier formulated the mathematical law of heat conduction in his landmark 1822 work 'Théorie analytique de la chaleur' (The Analytical Theory of Heat). He showed that the rate of heat flow is proportional to the temperature gradient, giving us what we now call Fourier's Law. He also invented Fourier series — a method of representing any periodic function as a sum of sines and cosines — which he developed specifically to solve heat diffusion equations and which became one of the most powerful tools in all of mathematics and engineering. Fourier spent years in Egypt as a scientific advisor during Napoleon's campaigns and became fascinated by the desert heat. Some historians believe his obsession with heat later in life (he reportedly kept his rooms extremely hot and wore heavy coats indoors) was connected to health problems he developed there — making him the rare scientist who literally lived his research.
Related Concepts
- Convection — Convection is the second major mechanism of heat transfer, occurring in fluids through bulk movement. Comparing it with conduction clarifies when each process dominates and why fluids are generally poor conductors but excellent convectors.
- Thermal Radiation — Radiation completes the trio of heat transfer mechanisms. Unlike conduction, it requires no medium at all and is governed by completely different physics (Stefan-Boltzmann Law), making the contrast instructive.
- Temperature and Thermal Energy — A solid understanding of what temperature and thermal energy mean at the molecular level is essential before conduction can make physical sense — temperature difference is literally what drives conductive heat flow.
- Electrical Resistance — Thermal resistance is mathematically analogous to electrical resistance. Understanding Ohm's Law and series/parallel resistors helps students analyse composite thermal systems using the same intuition.