Thermal physics

Conduction, convection, thermal radiation

Heat moves from hot to cold by conduction, convection, or radiation; multiple mechanisms can occur together.

Heat flows spontaneously from hotter to cooler regions. Conduction transfers energy through material interactions, convection carries it with bulk fluid motion, and radiation uses electromagnetic waves and needs no medium.

\dot Q_{\text{cond}} = kA\frac{T_h-T_c}{L}, \qquad P_{\text{rad}}=\epsilon\sigma A(T^4-T_{\text{env}}^4)

Definition: Three mechanisms

Conduction is often prominent in solids; convection occurs in fluids; thermal radiation is emitted by bodies above 0 K. The conduction equation is a steady flat-layer model; $k$ is thermal conductivity.

Compare conduction through a bar, a convection current, and radiation from a hot surface.

Everyday examples

A metal spoon warms in hot soup mainly by conduction. Circulating water in a pot transfers heat by convection. The Sun warms Earth across space by radiation.

Example: Heat through a bar

A bar has $k=200$ W m⁻¹ K⁻¹, area $A=0.01$ m², length $L=0.5$ m, and end-to-end difference 10 K. Find ideal conduction power.

Solution

$\dot Q=kA\Delta T/L=200\times0.01\times10/0.5=40$ W.

Quick check

Several heat-transfer mechanisms often act together in a room. A metal spoon warms mainly by conduction when it touches a hot pot; air near a heater warms, becomes less dense, and rises in a convective current; energy from the Sun reaches Earth mainly by radiation through vacuum. Insulation reduces conduction by trapping still air or using a material with low thermal conductivity. Light-colored curtains and reflective surfaces can reduce absorbed solar radiation, whereas dark surfaces often absorb more. The transfer rate depends on area, temperature difference, thickness, and material properties. A thick coat does not create heat; it slows energy leaving the body. Simple heat-flow equations assume a particular geometry and steady conditions, so keep those model assumptions separate from the qualitative distinction among the three mechanisms.

A slice of toast illustrates coexisting mechanisms: a heating element transfers energy by radiation and warms moving air by convection, while direct contact with the tray conducts heat. To identify the dominant process in a situation, ask whether energy passes through material, is carried by moving fluid, or travels as electromagnetic waves.

Which mechanism transfers heat through a vacuum?

Convection involves bulk motion of which kind of matter?

References

Halliday, Resnick, Walker (2014). Fundamentals of Physics