Conduction

Conduction is heat transfer through molecular interactions within a material or between materials in contact. Energy diffuses from a higher-temperature region to a lower-temperature region without requiring the bulk material to move with it. In buildings, conduction is particularly relevant to heat travelling through walls, floors, roofs and structural members.

A fire can heat one side of a construction while the other side remains comparatively cool. Conduction through the construction then raises the temperature of the cooler side and can expose people, combustible contents or structural material there. The process also removes heat from hot smoke and flames into surrounding boundaries.

The rate of conduction depends on temperature difference, material properties, thickness, area and time. A steady calculation assumes temperatures no longer change, whereas a real fire produces changing surface and internal temperatures. Both views are useful, but they answer different questions.

How energy moves through a solid

Conduction occurs through microscopic energy transfer. In good electrical conductors, free electrons make an important contribution. In electrical insulators, lattice vibrations called phonons still allow substantial heat conduction. Imperfections scatter these carriers and diffuse their energy through the solid.

The direction of net heat flow is from hot to cold. A larger temperature gradient, meaning a larger temperature change over a given distance, drives more conductive heat flow under otherwise equal conditions. Cross-sectional area also matters because a larger area provides more parallel routes for energy transfer.

Conduction transfers energy through a stationary solid. Based on Rockett and Milke (2002), p. 1-28.

Conduction does not require a visible opening or a flowing fluid. A continuous solid can transmit heat across its thickness even when it prevents smoke from passing. This makes conductive exposure different from direct flame contact and from smoke movement through gaps.

Heat can also be conducted within gases and liquids, although fire assessments often emphasise movement of those fluids as well. At a stationary surface, the fluid immediately adjacent to it has little or no bulk velocity, so molecular transfer remains part of the surface heat-exchange process.

Conductivity, heat capacity and diffusivity

Thermal conductivity expresses how readily a material conducts heat. A higher conductivity allows more heat flow for the same temperature difference, thickness and area. It is commonly expressed in watts per metre-kelvin, linking heat flow with distance and temperature difference.

Conductivity is not necessarily constant. Temperature, moisture and changes within the material can alter its thermal response; processing can also change conductivity. Some laminates, fibrous materials and reinforced products also conduct differently along and across their grain or layers. Such materials require direction-specific properties rather than one assumed value in every direction.

Specific heat capacity describes how much energy is needed to raise a unit mass by one degree. It affects how much thermal energy a material stores while its temperature rises. Conductivity concerns transmission through the material, while heat capacity concerns storage within it.

Thermal diffusivity combines conductivity, density and specific heat capacity. It describes how quickly a temperature disturbance can propagate through a material by conduction. Rockett and Milke identify square metres per second as its unit. A high diffusivity does not mean that the material stores more heat; it means that temperature changes penetrate more readily.

The distinction matters during a fire. One construction may accept heat slowly at its surface but transmit temperature changes efficiently, while another stores considerable energy near the exposed side. Material selection therefore needs more than a single conductivity value when transient exposure is assessed.

Thickness, layers and thermal resistance

For a uniform layer under steady, one-dimensional conditions, a thicker layer provides more resistance to heat flow. Van Rossum explains that doubling thickness doubles this resistance when conductivity remains unchanged. Doubling conductivity instead halves the resistance. These relationships describe the simplified steady model, not every transient fire exposure.

Thermal resistance offers a convenient way to describe several layers in series. Heat passing from one side of a composite construction to the other crosses each layer in turn. Under the steady model, the resistances of the layers can be added, just as electrical resistances in series are added.

Layer resistances add in the steady series model. Based on Van Rossum (2027), §5.2.

This approach makes the contribution of an insulating layer visible. A thin layer of low-conductivity material can provide substantial resistance, while a thicker layer of highly conductive material may provide less. Interface conditions and surface heat transfer still surround the conductive path.

Real constructions can depart from the simple layered model. In a framed wall, heat can cross through studs as well as insulation between them. Rockett and Milke demonstrate how these parallel paths change the effective heat flow. Their cavity-wall example requires a two-dimensional solution for a complete treatment.

Equations and a worked example

For a uniform slab, the conductive heat flux equals conductivity multiplied by the temperature difference and divided by thickness. This is the steady, one-dimensional form of Fourier's law. The total heat-transfer rate is the flux multiplied by the area. Positive heat flow below is from the hotter surface to the cooler surface.

$${\dot{q}}^{″}=\frac{\lambda }{L}(T_{s,h}-T_{s,c}),\dot{Q}={\dot{q}}^{″}A$$

Symbol	Description	Unit
${\dot{q}}^{″}$	Conductive heat flux	W/m²
$\dot{Q}$	Total heat-transfer rate	W
$\lambda$	Thermal conductivity	W/(m·K)
$L$	Layer thickness	m
$T_{s,h},T_{s,c}$	Hot and cold surface temperatures	K or °C
$A$	Area normal to heat flow	m²

For several layers, their resistances add. If convection at both outer surfaces is also included, the temperature difference refers to the gases on either side. Each convective surface resistance is the reciprocal of its heat-transfer coefficient. Radiation is a separate boundary contribution and is not included by these convective resistances alone.

$$R_i=\frac{L_i}{{\lambda }_i},R_s=\frac{1}{h_c},{\dot{q}}^{″}=\frac{T_{g,h}-T_{g,c}}{R_{s,h}+\sum _i{R}_i+R_{s,c}}$$

Symbol	Description	Unit
$R_i$	Resistance of material layer $i$ per unit area	m²·K/W
$R_{s,h},R_{s,c}$	Hot and cold convective surface resistances	m²·K/W
$h_c$	Convective heat-transfer coefficient at the relevant surface	W/(m²·K)
$T_{g,h},T_{g,c}$	Hot and cold gas temperatures	K or °C

Van Rossum illustrates the method with an insulated steel roof. Two steel sheets, each 0.5 mm thick, enclose 100 mm of polyurethane foam. The assumed conductivities are 45.8 W/(m·K) for steel and 0.034 W/(m·K) for the foam. Gas temperatures are 400 °C underneath and 10 °C outside, with both convective coefficients taken as 25 W/(m²·K).

The foam resistance is approximately 2.94 m²·K/W, while each steel sheet contributes only 0.0000109 m²·K/W. Each surface resistance is 0.04 m²·K/W. Adding the five resistances and dividing the 390 K temperature difference by their total gives the following result. The calculation retains unrounded resistances until the final step.

$${\dot{q}}^{″}=\frac{400-10}{0.04+0.0005/45.8+0.1/0.034+0.0005/45.8+0.04}\approx 129\mathrm{W}/{\mathrm{m}}^{\mathrm{2}}$$

This result illustrates the resistance method under fixed properties and steady conditions. It is not evidence that the foam or complete roof survives that fire exposure. Decomposition, changing properties and radiation are outside this simplified calculation. A fire-resistance assessment also requires the actual construction's thermal and mechanical behaviour over time.

Heating over time

A steady state develops only after boundary conditions have remained constant long enough for the internal temperature distribution to stop changing. During the early stage, energy entering the solid changes both its stored energy and its temperature distribution. The surface can become hot while deeper material remains close to its initial temperature.

Transient conduction changes the temperature distribution through a solid. Based on Rockett and Milke (2002), p. 1-29.

The required initial condition includes temperature throughout the solid. Boundary conditions specify either surface temperature or heat flux at each part of its boundary over time. These inputs distinguish one conduction problem from another and cannot be replaced by a material name alone.

Thermally thin and thick materials describe different responses to heat penetration. A thermally thin object can be approximated as having relatively little internal temperature variation, while a thermally thick object retains important gradients through its depth. This is a response classification that depends on heating duration, not simply geometric thickness.

For a solid with constant properties, one-dimensional conduction and no internal heat generation, the transient equation connects temperature change with the curvature of the temperature profile. Thermal diffusivity combines conductivity with the material's ability to store energy. The equation describes how the profile evolves; it does not supply the initial or boundary conditions.

$$\frac{\partial T}{\partial t}=\alpha \frac{{\partial }^{2}T}{\partial x^2},\alpha =\frac{\lambda }{\rho c}$$

Symbol	Description	Unit
$T$	Material temperature	K or °C
$t$	Time	s
$x$	Distance through the material	m
$\alpha$	Thermal diffusivity	m²/s
$\rho$	Material density	kg/m³
$c$	Specific heat capacity	J/(kg·K)

Physical and chemical changes add further transient effects. Moisture can evaporate in one region, diffuse and condense elsewhere, removing and releasing energy at different locations. Decomposition and other internal changes can also act as heat sources or sinks. The simple conduction equation then needs additional terms and data.

Conduction and fire resistance

Fire resistance concerns the ability of a construction or member to perform required functions during fire exposure. Conduction influences the temperatures that determine separation and structural response. A barrier can remain intact against flames yet still transmit enough heat to affect its unexposed side.

For separating constructions, conductive heat flow can raise the temperature of adjacent rooms and combustible objects. For load-bearing members, the evolving internal temperature affects material properties and structural behaviour. These are different performance questions, even when both use the same heat-transfer physics.

Conduction also removes energy from the fire environment. Hot gases transfer energy to walls and ceilings, and the solid then conducts part of it away or stores it. This boundary loss can influence gas temperature while simultaneously creating an exposure problem elsewhere.

An assessment should identify the quantity of interest. Heat flow through an entire area, heat flux per unit area, internal temperature and unexposed-surface temperature are not interchangeable. The required performance criterion determines which result matters and how detailed the temperature calculation must be.

Interpreting conductive calculations

A conductive Heat transfer result begins with a defined temperature difference. For differences, a change of one kelvin equals a change of one degree Celsius, so either scale can express the same driving difference. Absolute temperature must nevertheless be used where another relationship, such as gas density or radiation, requires it.

Heat flux and total heat flow answer different questions. Heat flux describes energy per unit area, while total heat flow adds the contribution over the whole exposed area. Comparing two constructions only by total watts can therefore mislead when their exposed areas differ. The relevant area and orientation must accompany the result.

The surface temperatures used in a conduction model are not automatically equal to adjacent gas temperatures. Convection and radiation connect each gas environment to the surface, after which conduction acts within the solid. Surface resistance and solid resistance therefore belong to different parts of the wider heat-flow path.

Layer resistances provide insight into where temperature changes occur under steady conditions. A larger share of the total resistance produces a larger share of the temperature drop in the simple series model. This can help identify whether a finish, insulation layer or structural layer controls transmission, without requiring every interface temperature as an initial input.

For wood and reinforced plastics, conductivity along the fibres may differ from conductivity across them. A layered assembly can therefore need properties for the direction of the actual heat flow. Replacing these with one average value adds an approximation to the model.

Changes within heated materials

Moisture changes both energy storage and transport inside porous solids. Evaporation absorbs energy at a heated location, while condensation can release energy at a cooler location after moisture diffuses through the material. The resulting heat-flow pattern is not captured by dry, constant-property conduction alone.

Temperature-dependent conductivity creates a related difficulty. A value obtained near ambient conditions may not represent the same material during a severe fire. Density, specific heat and internal structure can also change, altering both the resistance and the energy needed to raise temperature.

Char formation and decomposition introduce moving boundaries and internal heat effects. Newly formed layers can have different conductivity and thickness from the original material. Treating the original section as unchanged throughout exposure can therefore miss both insulation and consumption mechanisms.

Conductive loss to boundaries also feeds back into the fire environment. Energy entering walls and ceilings is no longer available to heat the room gas at that moment, but the stored energy can later affect surfaces and contents. Boundary conduction is thus part of the compartment energy balance, not merely an external detail.

Construction details can alter both heat flow and the barrier function. Framing creates parallel conductive paths, while cracks or holes can allow hot gases through the assembly. These mechanisms are absent from the ideal continuous-slab model. The insulation and integrity criteria of fire resistance therefore address different aspects of performance.

Limits and common misunderstandings

Conduction is not the movement of warm material from one room to another. It is energy transfer within or between materials. Smoke crossing an opening transports mass as well as energy, whereas a wall can conduct heat without any wall material crossing to the other side.

A low-conductivity material is not automatically a suitable fire barrier. Performance also depends on thickness, joints, thermal stability, decomposition, structural behaviour and exposure duration. Conductivity alone says nothing about whether the construction will remain intact.

Nor does a cool surface prove that negligible heat has entered the construction. Energy may be stored within a thick section or consumed by moisture evaporation and decomposition. The full temperature field and time history can matter more than one surface reading.

Steady calculations can estimate an order of magnitude, but Van Rossum emphasises that real fires are transient. Fire power, smoke temperature and receiving-surface temperature all change. Using a steady result as a complete fire-duration prediction would exceed the model's stated purpose.

A reliable calculation also preserves the direction of heat flow. The hot and cold surface labels must correspond to the scenario, and a negative intermediate value should not be hidden by taking an unexplained absolute number. Direction matters when assessing whether a boundary gains or loses energy.

Material data need the same dimensional check as the result. Conductivity is per unit length and temperature difference, whereas heat flux is per unit area. Mixing these quantities, or entering thickness in millimetres while the property is expressed per metre, changes the answer even when the physical description is correct.

See also

• Biot number

References

• Atreya, A. (2002). Convection heat transfer. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-44–1-72). National Fire Protection Association.
• Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). International fire engineering guidelines (2005 ed.). Australian Building Codes Board.
• Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
• Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
• Rockett, J. A., & Milke, J. A. (2002). Conduction of heat in solids. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-27–1-43). National Fire Protection Association.
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.