Conduction convection and radiation

Heat transfer is the transport of internal energy from a body at higher temperature to one at lower temperature.

Conduction occurs through the interaction and collisions of particles of matter, so it is possible in solids, liquids, and gases but not in a vacuum. The heat passing through a flat wall is described by Fourier's law:

$$Q = \frac{\lambda A \Delta T t}{d},$$

where $\lambda$ is the thermal conductivity, $A$ is the area, $d$ is the thickness, and $t$ is the time.

Convection is energy transport by flows of liquid or gas that arise because of density differences between heated and cooler layers; it is possible only in fluids. Radiation is energy transport by electromagnetic waves, which needs no medium and can occur in a vacuum; for example, the Sun's energy reaches Earth through space. In real processes these mechanisms often act simultaneously, but one may dominate.

Heat passes through a window pane of area $A = 1.5\ \text{m}^2$ and thickness $d = 4\ \text{mm}$. The temperature difference between the inner and outer surfaces is $\Delta T = 20\ \text{K}$, and the thermal conductivity of glass is $\lambda = 0.8\ \text{W/(m·K)}$. How much heat passes through the pane in $t = 1\ \text{h}$? Assume a steady process.

A house wall has area $A = 20\ \text{m}^2$, thickness $d = 0.25\ \text{m}$, and thermal conductivity $\lambda = 0.7\ \text{W/(m·K)}$. The inside temperature is $t_1 = 20\ ^\circ\text{C}$ and the outside temperature is $t_2 = -10\ ^\circ\text{C}$. Find the heat-loss power due to conduction alone. Explain why the real losses may be larger.

A spacecraft is in a vacuum and generates internal power $P = 500\ \text{W}$. The outer surface area is $A = 2\ \text{m}^2$, and the emissivity is $\varepsilon = 0.8$. Describe which heat-transfer mechanisms can remove heat from the spacecraft and which are impossible. Estimate the equilibrium surface temperature if it radiates to deep space, taking the space temperature to be close to $0\ \text{K}$. Use $P = \varepsilon \sigma A T^4$, $\sigma = 5.67 \cdot 10^{-8}\ \text{W/(m}^2\text{·K}^4)$.

Safe self-study investigation.

Simulation: open an interactive heat-transfer model (e.g., PhET “Heat Transfer” or similar) and observe how heat spreads through a solid, how a convection loop forms in a fluid, and how radiation carries energy through a vacuum. For each mechanism, record: (1) whether a medium is needed, (2) what carries the energy, (3) how the temperature difference affects it.

Safe home experiment: pour warm (not boiling) water into two identical mugs. Wrap one in light paper and the other in dark paper. Measure the temperature after 5 and 10 minutes. Explain why the dark surface may cool differently. Do not use boiling water or an open flame.

Show the three heat-transfer mechanisms side by side and highlight their key differences: the need for a medium, the microscopic energy carrier, and the role of temperature difference.

A three-panel diagram.

Left: a metal rod heated at one end; particles are shown as circles with vibration arrows, and collision arrows go from the hot end to the cold end. Label: “conduction, $Q = \frac{\lambda A \Delta T t}{d}$”.

Center: a vessel with liquid; near the heater at the bottom the liquid rises, and near the cold wall it sinks, forming a closed loop with arrows. Label: “convection, only in a fluid”.

Right: the Sun, with wavy arrows through empty space (vacuum) to Earth. Label: “radiation, no medium needed”.

While soup is boiling, the water in the pot is at about $100\ ^\circ\text{C}$. A metal spoon left in the pot heats up so that after $2\ \text{min}$ the handle near the upper end reaches $45\ ^\circ\text{C}$, even though the kitchen air is only $22\ ^\circ\text{C}$.

Heat from the hot water is transferred to the spoon by conduction: rapid atomic vibrations and free electrons in the metal pass internal energy along the spoon. In the water itself, convection operates: heated layers rise and cooler layers sink. Radiation from the stove and water also warms nearby surfaces.

A smartphone draws $5\ \text{W}$ while gaming and warms to $42\ ^\circ\text{C}$ at a room temperature of $22\ ^\circ\text{C}$. Its aluminium body with area $0.01\ \text{m}^2$ transfers heat to the air; without this removal the chip temperature would exceed $80\ ^\circ\text{C}$.

Inside the phone, heat moves by conduction from the chip to the case. From the case surface, energy is carried away by convection: air near the warm surface becomes less dense and rises, while cooler air takes its place. Part of the energy leaves by radiation in the infrared range because the case is warmer than the room.

Tea at $90\ ^\circ\text{C}$ is poured into a thermos; after $4\ \text{h}$ its temperature drops to $70\ ^\circ\text{C}$ at a kitchen temperature of $20\ ^\circ\text{C}$. The glass flask has double silvered walls, and the air between them is pumped out.

The vacuum between the walls almost eliminates conduction and convection: there are few particles to transfer energy or form flows. The silver coating reduces radiation by reflecting infrared waves back toward the tea. The remaining heat loss occurs through the stopper and thin walls.