Thermal conductivity

Thermal conductivity is the material property that describes how well a material conducts heat. It is the heat flow per unit area through a material for each kelvin of temperature difference per metre of thickness, and its unit is W/(m·K). Introduction to Fire Safety Engineering uses the symbol λ (lambda), while the SFPE Handbook uses k. Values span a very wide range. Copper has a thermal conductivity of 387 W/(m·K) and steel 45.8 W/(m·K), while concrete has 2.0 W/(m·K) and polyurethane foam only 0.034 W/(m·K).

In fire safety engineering, thermal conductivity determines how fast heat passes through walls, floors, roofs and fire protection. It also determines how quickly the temperature rises inside a structural member. A material with a low conductivity, such as an insulation board or a sprayed fire-resistive material, slows the heating of what lies behind it. Thin parts made of a material with a high conductivity, such as steel, warm almost uniformly through their thickness.

Together with density and specific heat capacity, thermal conductivity sets the thermal diffusivity and the thermal inertia of a material. These combined properties describe how fast heat penetrates and how quickly a surface heats up. Thermal conductivity is not a fixed number. For most building materials it changes with temperature, moisture content and porosity, and measured values can differ considerably between laboratories.

Definition and Fourier's law

Heat conduction is the transfer of heat between the molecules within a material. Fourier quantified the process in 1812. His law states that the heat transferred per unit time across an area is proportional to that area and to the temperature gradient. The heat flows from the hotter to the cooler part. Thermal conductivity is the constant of proportionality in this law.

Why some materials conduct far better than others depends on how the heat is carried. In 1853 Wiedemann and Franz observed that the electrical and thermal conductivities of metals are proportional. This suggests that free electrons carry most of the heat in good electrical conductors. NIST confirms that in steel above room temperature, conduction by electrons dominates. In general, the conductivity of a material can also differ between directions and vary with position. Rockett and Milke assume for simplicity that it is the same in all directions and independent of temperature.

For a flat layer of uniform material in a steady state, the heat flux through every plane of the layer is the same. With a constant conductivity, the temperature profile through the layer is therefore a straight line. The heat flux through the layer then follows from the thermal conductivity, the temperature difference and the thickness:

Steady conduction through a uniform layer: the temperature falls linearly from T1 to T2, and the heat flux is λ(T1 − T2)/L. Based on Van Rossum (2027), §5.2, and Rockett and Milke (2002), p. 1-30.

$${\dot{q}}^{″}=\frac{\lambda }{L}\cdot (T_1-T_2)$$

Symbol	Description	Unit
${\dot{q}}^{″}$	heat flux through the layer	W/m²
$\lambda$	thermal conductivity (written k in the SFPE Handbook)	W/(m·K)
$L$	thickness of the layer	m
$T_1$	surface temperature on the heated side	K or °C
$T_2$	surface temperature on the cool side	K or °C

The relation assumes that the thermal conductivity is constant. In reality it often depends on temperature, so the calculation is a simplification. Because only a temperature difference appears, degrees Celsius may be used as well as kelvin. The ratio of thickness to conductivity is the thermal resistance of the layer, in m²·K/W. A layer twice as thick has twice the resistance, and a material with twice the conductivity has half the resistance. Resistances of layers in series can be added, in the same way as electrical resistances.

Worked example

Rockett and Milke calculate the heat flow through a wall made of two sheets of 15.9 mm gypsum board on timber studs. The hot surface is at 200 °C and the cold surface at 20 °C. They take thermal conductivities of 0.8 W/(m·K) for gypsum board, 0.17 W/(m·K) for wood and 0.04 W/(m·K) for glass-fibre insulation.

Without a cavity, the two boards back to back would conduct about 4.5 kW/m². This is 0.8 × 180 / 0.0318 W/m², or about 4,530 W/m². With a 92.1 mm cavity filled with insulation and studs, the effective conductivity of the cavity is 0.0532 W/(m·K). The heat flux through the wall then drops to about 0.10 kW/m². The insulation still conducts most of the heat because it fills most of the area, while the studs carry about 30 %. The gypsum boards add little resistance compared with the insulation.

The example also shows that conduction is not the only path. If the cavity were empty, radiation and convection across it would dominate. With radiation alone and an emissivity of 1.0, the effective conductivity of the empty cavity would be about 1.17 W/(m·K), more than ten times that of the insulated cavity.

Introduction to Fire Safety Engineering gives a similar example for a facade. The facade consists of 150 mm of polyurethane foam between two leaves of 65 mm masonry, with a fully developed fire of 900 °C inside and 20 °C outside. The thermal resistance of the foam layer, 4.41 m²·K/W, makes up most of the total resistance of 4.74 m²·K/W. The temperature drop over each part is proportional to its resistance, so the hot face of the foam reaches about 875 °C. In a steady state, the heat flux through this facade would be about 186 W/m². The book's 4 mm steel roof under a smoke layer of 634 °C, in contrast, passes about 7,670 W/m², because steel offers almost no resistance.

Steady temperature profile through a facade of 65 mm masonry, 150 mm polyurethane foam and 65 mm masonry, with a 900 °C fire inside and 20 °C outside. Based on Van Rossum (2027), §5.2.

Typical values

Introduction to Fire Safety Engineering gives a table of thermal properties of common materials. Metals conduct heat best: 387 W/(m·K) for copper and 45.8 W/(m·K) for steel. Mineral materials lie between 0.48 and 2.0 W/(m·K): 2.0 for concrete, 0.76 for float glass, 0.69 for masonry and 0.48 for gypsum plaster. Wood and plastics have low values, such as 0.19 W/(m·K) for PMMA, 0.17 for oak and 0.14 for spruce. Polyurethane foam reaches 0.034 W/(m·K), and still air 0.026 W/(m·K). Steel thus conducts heat more than 1,300 times better than polyurethane foam.

Thermal conductivity of common materials at room temperature, on a logarithmic scale. Based on Van Rossum (2027), §5.5.

Other sources show how much values vary within one class of material. For carbon steels the conductivity usually lies between 46 and 65 W/(m·K). In the NIST investigation of the World Trade Center, data for twelve low-alloy steels spanned 40 % of the mean value even near room temperature. The microstructure of the steel affects the conductivity, so there is no general relation between steel grade and conductivity. For concrete, the conductivity depends mainly on the aggregate. Concretes with dense crystalline aggregates, such as quartz, conduct better than those with porous aggregates.

For wood, White gives a relation in which the conductivity across the grain rises with density and moisture content. It is valid for densities above 300 kg/m³, moisture contents up to 25 % and a temperature of 24 °C. For wood of 500 kg/m³ with 12 % moisture, it gives about 0.14 W/(m·K). Conductivity along the grain is 1.5 to 2.8 times higher, and it increases by about 2 to 3 % per 10 °C. Plasterboard of about 700 kg/m³ has a typical conductivity of 0.25 W/(m·K).

Sprayed fire-resistive materials are designed for very low conductivity. Manufacturers reported 0.042 and 0.043 W/(m·K) at 24 °C for the two BLAZE-SHIELD products used in the World Trade Center towers. For electrical cable bundles in nuclear power plants, measured values were 0.15 W/(m·K) for 3-conductor cables and 0.18 W/(m·K) for single-conductor cables. The bundle with more copper had the higher conductivity.

Behaviour at high temperatures

Strictly, heat moves by conduction alone only in solids without pores that do not transmit radiation. Most building materials are porous. In them, heat is transmitted by a combination of conduction, radiation and convection in the pores. The thermal conductivity of a porous material is therefore an empirical factor that allows Fourier's law to describe the overall heat transmission. In insulation foam or mineral wool, part of the heat transfer is by radiation, which is included in the λ-value of the material.

At high temperatures, radiation through the pores becomes more important. The measured conductivity then depends on the temperature gradient used in the test, which explains large discrepancies between laboratories. Moisture in a material migrates under a temperature gradient and raises the apparent conductivity. Because heating causes irreversible changes in the microstructure, the conductivity usually differs between heating and cooling.

The conductivity of most building materials depends strongly on temperature. In the World Trade Center investigation, the measured conductivities of the sprayed fire-resistive materials increased with temperature up to 1,200 °C. For gypsum panels, the conductivity first decreased up to 200 °C and then increased above 300 °C. Charring, melting, intumescence and burning away also change the thickness and the local conductivity of a building element during a fire.

Use in fire safety engineering

Thermal conductivity strongly influences the fire resistance of separating and load-bearing elements. Concrete is non-combustible and has a low thermal conductivity, so the inner core of a concrete member stays cool and continues to carry load. This behaviour is described further in concrete in fire. Wood also has a low conductivity. When the base of the char layer is at about 300 °C, the wood 6 mm further in is at only about 180 °C.

Fire protection of steel relies on the same property. One class of sprayed fire-resistive materials protects the steel by providing a layer of low conductivity, such as mineral fibres. The other class contains cementitious materials with chemically bound water, which absorb energy as the water is released. In the NIST fire tests, the temperature at the surface of the insulation rose faster than at the surface of bare steel, because of the far lower conductivity of the insulation. The typical uncertainty of conductivity measurements for such materials was ±6 %. The calculated steel temperatures were sensitive to the insulation thickness and conductivity.

Thermal conductivity also enters compartment fire calculations through the thermal properties of the enclosure. In the McCaffrey method for the hot gas layer temperature, as presented in the International Fire Engineering Guidelines (2005), heat loss to the walls is described by an effective heat transfer coefficient. After the thermal penetration time, this coefficient equals the conductivity of the wall divided by its thickness. Before that time, it depends on conductivity, density and specific heat together. In Lie's calculated fire curves, heavy bounding materials have a conductivity of 1.16 W/(m·K) and light ones 0.58 W/(m·K).

In New Zealand, C/VM2 (second edition, 2025) calculates the time equivalence of a fire with a factor that depends on the lining. That factor is based on the square root of the product of conductivity, density and specific heat. Typical values of this property range from 400 J/(m²·s^0.5·K) for very light insulating materials to more than 2,500 for thin sheet steel. Only the first few centimetres on the fire-exposed side are relevant for this calculation. Fire models such as CFAST and the Fire Dynamics Simulator need the thermal conductivity of solid surfaces as an input, together with density, specific heat and emissivity. In the sensitivity study of the zone model MAGIC, for example, concrete was given a conductivity of 1.75 W/(m·K).

Limits and common misconceptions

A common misconception is that thermal conductivity is a fixed property of a material. In fire conditions it varies with temperature, moisture and decomposition, and for porous materials it is only an empirical factor. For insulating materials with a porosity of 0.8 or higher, conduction through the solid may be an insignificant part of the heat transfer. Applying Fourier's law may then lead to misleading conclusions.

A second misconception is that a low conductivity alone means slow heating at the surface. The surface temperature depends on the thermal inertia, which combines conductivity with density and specific heat. A light insulation material can therefore become hot at its surface very quickly, which can contribute to rapid ignition if it is combustible.

The steady-state relation also does not describe the first phase of a fire. Before heat has reached the back face of a thick element, a steady calculation overestimates the heat flow through it. The book shows that a 200 mm concrete wall behaves as thermally thick during the first 15 minutes of a fire. Twice the characteristic penetration depth is then only about 0.060 m.

See also

• Biot number
• Heat flux
• Thermally thin and thick materials

References

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