Physics › 🔥 Thermodynamics

Heat Transfer

Why a metal railing feels colder than a wooden fence, even on the very same winter morning.

High school
💡
The big idea: Heat always moves from hot to cold, and it does so in exactly three ways: conduction (through touching matter), convection (carried by moving fluid), and radiation (electromagnetic waves that need no medium at all). Once you can spot which mechanism is doing the work in a given situation — a frying pan, a breeze, sunlight — thermodynamics stops feeling abstract and starts explaining your everyday world.
🎯 By the end, you'll be able to
  • Explain how conduction, convection, and radiation each transfer thermal energy, and identify which one dominates in a given real-world situation.
  • Use Fourier's law and Newton's law of cooling to calculate rates of heat flow through real materials.
  • Distinguish thermal conductors from insulators and explain why materials at the same temperature can feel very different to the touch.
  • Apply these ideas to explain everyday phenomena: home insulation, staying warm, and the greenhouse effect.
📎 You should already know
  • Temperature and Thermal Energy
  • Energy, Work, and Power Basics
  • States of Matter

Three Ways Heat Travels

Grab a metal spoon and a wooden spoon and dip both in the same bowl of hot soup. Within seconds the metal spoon's handle is uncomfortably warm; the wooden one barely changes. Both spoons sit in soup at the exact same temperature — so why the difference? Meanwhile, across the room, a heater warms the air near the floor, which rises and spreads warmth throughout the space without anything touching you. And outside, sunlight crosses 150 million kilometers of empty space and warms your face the instant it hits your skin. Three completely different situations — one shared reason heat moves at all, and three distinct mechanisms for how it gets there: conduction, convection, and radiation.

🔑 The One Rule Heat Always Obeys

Thermal energy always flows spontaneously from a hotter object or region to a colder one — never the reverse, on its own. Every heat-transfer story is really this one rule playing out through a different mechanism:

  • Conduction — heat passes directly between touching particles, like a chain of jostling dominoes.
  • Convection — heat rides along with a moving fluid (air or liquid) as warmer, less dense fluid rises and cooler fluid sinks in to replace it.
  • Radiation — heat travels as electromagnetic waves, needing no matter in between at all.
\[ \frac{Q}{t} = \frac{kA\Delta T}{d} \]
Fourier's law of conduction: the rate of heat flow \(Q/t\) depends on the material's thermal conductivity \(k\), the cross-sectional area \(A\), the temperature difference \(\Delta T\) across the material, and its thickness \(d\). Bigger \(k\) or \(A\), or a thinner slab, all speed up heat flow.
\[ \frac{Q}{t} = hA\Delta T \]
Newton's law of cooling for convection: heat flow depends on a convective heat-transfer coefficient \(h\) (which grows with air or fluid movement — a fan or breeze increases \(h\)), the exposed area \(A\), and the temperature difference \(\Delta T\) between the surface and the surrounding fluid.
\[ P = \epsilon \sigma A T^4 \]
The Stefan-Boltzmann law of radiation: every object radiates power \(P\) proportional to the <i>fourth power</i> of its absolute temperature \(T\) (in kelvin), scaled by its surface area \(A\), its emissivity \(\epsilon\) (0 to 1, how efficiently the surface radiates), and the constant \(\sigma = 5.67\times10^{-8}\ \text{W/(m}^2\text{K}^4\text{)}\).
🎮 Interactive: Conduction, Convection, and Radiation in Action LIVE
Change the material, thickness, and temperature difference and watch how each heat-transfer mode responds differently.

Why Metal Feels Colder Than Wood

Back to that spoon: metal has a high thermal conductivity \(k\) — its atoms are packed in an orderly lattice with free-roaming electrons that shuttle energy along almost instantly. Wood and plastic have a much lower \(k\) because they lack those free electrons — heat can only hop sluggishly from molecule to molecule. Foam-like materials are even better insulators because they also trap tiny pockets of still air, and still air is one of the worst conductors around. So when your hand touches metal at room temperature, heat conducts out of your hand rapidly, and it feels cold — even though the metal isn't actually colder than the wood beside it. This is exactly why a goose-down jacket or fiberglass wall insulation work so well: they trap air in place so it can't conduct (or convect) heat away efficiently. A layer of body fat helps the same way for a different reason — fatty tissue itself conducts heat poorly and has relatively little blood flow, so it slows the transfer of heat away from the body's core.

📝 Worked example: A single-pane glass window (thermal conductivity k = 0.8 W/(m·K)) has an area of 2 m² and is 5 mm (0.005 m) thick. Indoors is 20°C and outside is 0°C. How much heat escapes through this window every second?
  1. A temperature difference in °C is the same size as in kelvin, so ΔT = 20°C − 0°C = 20 K.
  2. Apply Fourier's law: Q/t = kAΔT/d.
  3. Q/t = (0.8)(2)(20) / 0.005 = 32 / 0.005.
  4. Q/t = 6400 W.
✓ About 6400 watts (6.4 kW) of heat pour through that single window every second — more continuous power than a hair dryer. This is exactly why double-glazed windows, which trap an insulating air gap between two panes, cut heat loss so dramatically.
📝 Worked example: A mug of coffee has an exposed surface area of 0.05 m² and loses heat to the surrounding air with a convective heat-transfer coefficient h = 10 W/(m²·K). The coffee is at 90°C and the room air is at 20°C. What is the rate of heat loss by convection?
  1. ΔT = 90°C − 20°C = 70 K.
  2. Apply Newton's law of cooling: Q/t = hAΔT.
  3. Q/t = (10)(0.05)(70) = 35 W.
✓ The coffee loses about 35 watts to the air by convection alone. Blowing across the surface increases air movement — and therefore h — which is exactly why blowing on hot coffee cools it faster.
✨ The Greenhouse Effect Is Radiation, Twice Over

Sunlight (mostly visible light) radiates across space and passes fairly freely through the atmosphere to warm Earth's surface. That warmed surface then re-radiates energy of its own — but as infrared, since cooler objects radiate at longer wavelengths. And because power scales with the fourth power of temperature (\(P \propto T^4\)), Earth's much cooler surface radiates far less total power than the blazing Sun, even though both are radiating constantly. Greenhouse gases like carbon dioxide and water vapor are especially good at absorbing that outgoing infrared and re-radiating part of it back down toward the surface. The result: extra energy stays trapped near the ground. It's the same radiation physics from this lesson, just playing out on a planetary scale.

⚠️ Insulators Don't Block "Cold" — They Slow Down Heat

A common trap: thinking insulation "keeps the cold out." There's no such thing as cold flowing anywhere — cold is simply the absence of heat. An insulator (low \(k\)) just slows the rate at which heat flows through it, in whichever direction the temperature gradient points. That's why a thermos keeps hot cocoa hot and iced tea cold using the very same insulating shell. Also remember: convection requires a fluid to move, and conduction requires touching matter — only radiation crosses a true vacuum, which is how the Sun's warmth reaches you across empty space.

Check your understanding

1. Which mode of heat transfer can occur through the vacuum of space, with no medium at all?
Radiation travels as electromagnetic waves and needs no matter to travel through — that's how the Sun's energy crosses empty space to reach Earth.
2. A metal rod has k = 50 W/(m·K), a cross-sectional area of 0.01 m², a length of 2 m, and a 100 K temperature difference between its ends. What is the rate of heat conduction along the rod?
Using Q/t = kAΔT/d: Q/t = (50)(0.01)(100) / 2 = 50 / 2 = 25 W.
3. Two blocks — one metal, one wood — sit in the same room and both read 10°C on a thermometer. The metal block feels much colder to the touch. Why?
Both blocks are genuinely at the same temperature. Metal's high thermal conductivity pulls heat out of your warm skin much faster than wood's low conductivity does, so it feels colder even though it isn't.
4. Why do fiberglass wall insulation and a goose-down jacket both work well as thermal insulators?
Both materials work by trapping tiny pockets of air in place. Still air has very low thermal conductivity, so immobilizing it (stopping it from conducting or convecting freely) creates an effective barrier to heat flow.
✅ Key takeaways
  • Heat always flows from hotter to colder — spontaneously and only in that direction — through conduction, convection, or radiation.
  • Conduction transfers heat through direct particle contact (Q/t = kAΔT/d); metals conduct well, while air, foam, and wood conduct poorly.
  • Convection carries heat via bulk fluid motion (Q/t = hAΔT); radiation transfers heat as electromagnetic waves and is the only mode that works through a vacuum (P = εσAT⁴).
  • Insulators like fiberglass, down feathers, and body fat work by slowing heat's escape — trapped still air or low-conductivity tissue — they don't keep "cold" out, they just slow conduction down.