Heat Transfer — Conduction, Convection & Radiation

The three modes at a glance

When two regions are at different temperatures, the second law of thermodynamics dictates that heat flows spontaneously from the hotter to the colder until they equalise. Nature accomplishes this by three mechanisms only, and NEET expects you to distinguish them sharply: which need a medium, which involve bulk motion of matter, and which can cross a vacuum.

Conduction and convection both require matter as a transport medium and so cannot operate across the vacuum of space. Radiation is the lone mode that needs no medium — which is why the Sun's energy reaches us across roughly 150 million kilometres of empty space, and why we feel the warmth of a fire almost instantly, before slower convection currents in the air have had time to set in.

Conduction and the heat current

Take a metal rod of length $L$ and uniform cross-section $A$, with its two ends held at fixed temperatures $T_1$ and $T_2$ (with $T_1 > T_2$) by large reservoirs, and its sides insulated so no heat escapes laterally. After some time the rod reaches a steady state: the temperature falls uniformly along the rod, and heat enters the hot end at exactly the rate it leaves the cold end. The rate of heat flow — the heat current $H$ — is then constant along the rod.

Experiment shows $H$ grows with the area $A$ and the temperature difference, and falls with the length $L$:

The constant $K$ is the thermal conductivity of the material — the larger the $K$, the faster the material conducts. Numerically, $K$ is the heat conducted per second across a slab of unit area and unit thickness when its faces differ by one kelvin. Its SI unit is $\text{W m}^{-1}\,\text{K}^{-1}$ (equivalently $\text{J s}^{-1}\text{m}^{-1}\text{K}^{-1}$).

Thermal conductivity values

The single fact that separates a good conductor from an insulator is the magnitude of $K$. Metals conduct freely because their loosely-bound electrons shuttle energy efficiently; gases conduct poorly because their molecules are far apart. The table below uses the standard NIOS and NCERT figures — commit the ordering, not every decimal.

The low conductivity of trapped air explains everyday insulation. Wool keeps us warm because air is trapped between its fibres; two thin layers of cloth are warmer than one thick layer because they sandwich an extra insulating air gap; a thermocole box protects ice because $K_{\text{thermocole}} = 0.01\ \text{W m}^{-1}\text{K}^{-1}$ is the lowest in the table. NCERT Example 10.6 likewise gives a steel-copper junction temperature of 44.4 °C — the colder junction sits much nearer the high-conductivity copper end.

Thermal resistance: series and parallel

Rewriting $H = KA\,\Delta T / L$ as $\Delta T = H \cdot \dfrac{L}{KA}$ exposes a clean analogy with Ohm's law $V = IR$. The temperature difference plays the role of voltage, the heat current plays the role of current, and the quantity

is the thermal resistance of the slab, measured in K W⁻¹. A long, thin, poorly-conducting slab has high resistance. Because the analogy is exact, slab combinations follow the same rules as resistors.

For two identical-area, identical-length slabs joined end to end (series), the equivalent conductivity is the one used in Example 10.7: $K' = \dfrac{2K_1K_2}{K_1+K_2}$ — a harmonic-type mean dominated by the poorer conductor. For two slabs welded side by side (parallel) with equal cross-sections, the equivalent conductivity is the arithmetic mean $K_{\text{eq}} = \dfrac{K_1 + K_2}{2}$, exactly the NEET 2017 welded-rod result below.

Convection: natural and forced

Convection transfers heat by the actual motion of matter and so is possible only in fluids — liquids and gases. When a fluid is heated from below, the warm portion expands, becomes less dense, and is pushed upward by buoyancy; cooler, denser fluid sinks to replace it. The descending fluid is heated in turn, and a continuous convection current is established. Drop a few grains of potassium permanganate into a heated flask of water and the looping current becomes visible as coloured streaks.

Convection comes in two varieties. In natural (free) convection, gravity does the work: buoyancy alone drives the loop, so it cannot occur in free fall or in an orbiting satellite where there is no effective gravity to separate hot and cold fluid. In forced convection, a pump or fan moves the fluid mechanically — examples include forced-air home heating, an automobile's engine-cooling system, and the human heart circulating blood to keep the body at a uniform temperature. There is no simple equation for convection as there is for conduction; the rate depends on the surface area and the temperature difference in a complicated way.

Sea breeze, land breeze and trade winds

Natural convection on a planetary scale produces several phenomena NEET likes to test. Each turns on water's large specific heat capacity, which makes land heat and cool faster than the adjacent sea.

The sea breeze is the convection cycle you feel as a cool draught walking along a shore on a hot afternoon: the land warms quickly, the air above it rises, and denser air from over the cooler sea moves in to fill the gap. At night the land radiates its heat away faster than the sea, the sea becomes the warmer surface, and the cycle reverses into a land breeze. The trade wind is the same buoyancy mechanism stretched across the globe — hot equatorial air rises and would simply flow to the poles, but the Earth's rotation (the equatorial surface moving east at roughly 1600 km/h while the poles move at zero) deflects the descending air so it returns to the equator from the north-east.

Radiation and the blackbody

Radiation is the transfer of energy by electromagnetic waves, which travel at $3 \times 10^8\ \text{m s}^{-1}$ and require no medium at all. Every body, solid, liquid or gas, continuously emits this thermal radiation by virtue of its temperature, and continuously absorbs the radiation falling on it. When a body is at the same temperature as its surroundings the two rates balance and there is no net change; a hotter body loses energy on balance, a cooler body gains it.

A blackened platinum wire heated by a rising current illustrates how the emitted radiation changes with temperature. Below about 525 °C the wire emits only invisible heat; at 525 °C it begins to glow dull red, then cherry red near 900 °C, orange near 1100 °C, yellow near 1250 °C, and white near 1600 °C. Two lessons follow: the colour of a glowing body reveals its temperature, and as temperature rises the emission shifts towards shorter wavelengths.

A perfectly black body is an idealisation that absorbs all radiation falling on it (absorptivity $a = 1$, reflectivity and transmissivity both zero) and, at any temperature, emits the maximum possible radiation. No real surface is perfectly black — lamp black absorbs about 96% of visible light, platinum black about 98% — but a small hole in a heated cavity behaves almost perfectly, since any ray entering is trapped by repeated internal reflection. The radiation spectrum of such a blackbody is universal: it depends only on temperature, not on the size, shape or material of the body.

The radiation laws

Three quantitative laws govern blackbody radiation. The first two follow directly from the spectrum in Figure 4; the third links emission to absorption.

The Stefan-Boltzmann law states that the energy radiated per second from a surface of area $A$ rises with the fourth power of the absolute temperature: $H = Ae\sigma T^4$, where $e$ is the emissivity (1 for a perfect radiator, about 0.4 for a tungsten lamp). The net loss when a body at $T_1$ sits in surroundings at $T_2$ is $H_{\text{net}} = Ae\sigma(T_1^4 - T_2^4)$. The fourth-power dependence is steep: doubling the Kelvin temperature multiplies the radiated power by sixteen.

Wien's displacement law, $\lambda_m T = 2.9\times10^{-3}\ \text{m K}$, fixes the wavelength of peak emission. Because the product is constant, a hotter body peaks at a shorter wavelength. The Sun's surface, near 6000 K, peaks in the visible; the Moon's surface peaks near 14 µm in the infrared, which by Wien's law implies a temperature of about 200 K. This law lets astronomers read the temperature of stars they can never reach.

Kirchhoff's law and emissivity

When radiation strikes a surface, the fractions reflected ($r$), absorbed ($a$) and transmitted ($t$) satisfy $r + a + t = 1$. The emissive power of a surface is the energy it radiates per second per unit area; the absorptive power is the fraction of incident energy it absorbs. Kirchhoff's law states that, at a given temperature and wavelength, the ratio of emissive power to absorptive power is the same for every body and equals the emissive power of a perfect blackbody. The plain reading: good absorbers are good emitters.

This single principle explains a cluster of NEET facts. We wear white in summer because a white (poorly absorbing) surface is also a poor emitter and stays cool; the blackened bottoms of cooking utensils absorb the maximum heat from the flame; the silvered, evacuated walls of a thermos minimise radiation loss because a polished surface is a poor emitter. The emissivity $e = E/E_b$ measures how close a real surface comes to a blackbody — it ranges from near 0 for a polished metal to 1 for lamp black, and it appears as the factor $e$ in the Stefan-Boltzmann power.

The greenhouse effect

The greenhouse effect ties the radiation laws together. Short-wavelength visible sunlight passes freely through the atmosphere (and through the glass of a greenhouse) and is absorbed by the Earth's surface. The warmed Earth then re-emits this energy — but because the Earth is far cooler than the Sun, Wien's law puts its emission peak in the long-wavelength infrared. Carbon dioxide and water vapour are transparent to visible light yet opaque to infrared, so they trap the outgoing radiation rather than letting it escape, and the surface warms. This natural effect keeps the planet habitable; the excess CO₂ released by burning fossil fuels intensifies the trapping and drives global warming, melting glaciers and raising sea levels.