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Thermal Conduction Calculator

Calculate the steady-state heat transfer rate through a wall using Fourier's law from conductivity, area, temperature difference, and thickness

Frequently Asked Questions

What is Fourier's law of conduction?

It states that heat flow through a wall is proportional to conductivity, area, and temperature difference, and inversely proportional to thickness.

How does thickness change heat loss?

Doubling the wall thickness halves the conducted heat flow, which is why thicker insulation reduces heat loss.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

Fourier's law of heat conduction describes how thermal energy flows through a solid wall. The rate of heat transfer is proportional to the thermal conductivity of the material, the cross-sectional area, and the temperature difference across the wall, and is inversely proportional to the wall thickness. Thicker walls and lower conductivity slow the flow.

How To Use It

Enter the thermal conductivity in watts per meter-kelvin, the area in square meters, the temperature difference between the two faces in kelvin or degrees Celsius, and the thickness in meters. The calculator returns the steady-state heat transfer rate in watts, which is the power conducted through the wall.

Conductivity Of Common Materials

Copper conducts heat very well at around 400 watts per meter-kelvin, while building insulation sits near 0.04. Choosing a low-conductivity material or a thicker layer reduces heat loss, which is the basis of insulating walls, windows, and pipes.

Tips

A temperature difference in Celsius equals the same difference in kelvin.
Doubling the thickness halves the heat flow.
Insulators have low conductivity values.

Thermal Resistance and R-Values

Thermal resistance is the opposition a material offers to the flow of heat, directly analogous to electrical resistance in a circuit. For a slab of material the resistance is R = L / (k × A), where L is thickness, k is thermal conductivity, and A is cross-sectional area. A higher R means less heat flows for the same temperature difference.

In building science, R-values are typically stated per unit area (m²K/W in SI, or ft²°F·h/BTU in US customary). A common residential wall assembly might layer 12.7 mm drywall (k ≈ 0.17), 89 mm glass-fiber batt (k ≈ 0.044), and 12 mm OSB sheathing (k ≈ 0.13). Because these layers are in series, their thermal resistances simply add together, just as series electrical resistors add. Parallel heat paths, such as wood studs alongside insulation, combine like parallel resistors and must be weighted by their area fractions.

ASHRAE 90.1, the commercial building energy standard, sets minimum assembly R-values by climate zone. For example, Climate Zone 5 requires R-20 or better for above-grade walls and R-38 for roofs. The label printed on insulation batts is the R-value per the installed thickness at standard conditions; compressing the batt reduces the effective R-value proportionally.

Material Selection in Practice

Metals span a wide range. Copper (385 W/m·K) and aluminum (205 W/m·K) are the preferred heatsink materials because they move heat away from electronics quickly. Steel sits near 50 W/m·K - useful where structural strength is needed alongside reasonable conductivity, as in heat exchanger tubes. Titanium offers only about 22 W/m·K, yet aerospace structures use it because its strength-to-weight ratio is outstanding and its lower conductivity is an acceptable trade-off in non-thermal applications.

Ceramics cover an enormous range. Alumina (Al&sub2;O&sub3;, roughly 30 W/m·K) and silicon carbide (SiC, roughly 120 W/m·K) are popular electronics substrate materials because they are electrical insulators while still conducting heat well enough to spread heat from power chips. In contrast, common firebrick sits below 1 W/m·K, making it an effective refractory liner.

Polymers are generally poor conductors (0.1 to 0.5 W/m·K), which makes them natural thermal insulators. This is why plastic handles on cookware stay cool, and why polymer foams are used for pipe lagging and building insulation. Aerogel is the extreme case: silica aerogel has a conductivity as low as 0.015 W/m·K at room pressure, lower than still air, because the nanoporous structure suppresses gas-phase conduction. Phase-change materials (PCMs) such as paraffin waxes add latent heat storage to a wall assembly: they absorb large amounts of heat while melting and release it on cooling, buffering daily temperature swings without changing the steady-state conductivity significantly.

Design Considerations and Limitations

This calculator assumes steady-state conduction: temperatures at both surfaces are fixed, the material properties are uniform, and enough time has passed that heat flow is constant throughout the wall. In transient situations, such as a furnace ramping up or a building warming after sunrise, the thermal mass (heat capacity) of the material matters, and a time-dependent analysis is needed. Fourier's transient equation introduces a second variable, thermal diffusivity (α = k / (ρ c_p)), which governs how quickly temperature changes propagate through the material.

Contact resistance at interfaces between materials is a common source of discrepancy between calculated and measured heat flow. Even surfaces that appear flat have microscopic asperities that create air gaps, and air is a poor conductor. Thermal interface materials (TIM) such as thermal grease, phase-change pads, and indium foil reduce contact resistance in electronics assemblies. In building construction, gaps between framing and insulation can similarly degrade real-world R-values well below the nominal label values.

Conduction is only one of three heat transfer mechanisms. Convection carries heat via fluid motion at surfaces (the h·A·ΔT term in overall U-values), and radiation exchanges energy as electromagnetic waves even across a vacuum. In high-temperature furnaces or in space applications, radiation often dominates, and treating conduction alone gives a significantly underestimated total heat loss. For a complete analysis, all three modes must be combined, often using finite element analysis (FEA) when geometry is complex.

Common Applications

Electronics heatsink sizing: A CPU or power transistor dissipates a known wattage; the heatsink must conduct that power to ambient air within an allowable junction temperature rise. Fourier's law gives a first estimate of the heatsink cross-section and fin length before detailed CFD modeling.
Pipe insulation: Industrial pipes carrying steam or chilled water lose (or gain) heat through their walls. Adding insulation of known conductivity and thickness directly reduces the calculated Q, lowering energy cost and preventing condensation on cold pipes.
Building envelope: Walls, roofs, and slabs are multi-layer assemblies. Architects and energy modelers use the series-resistance approach to ensure code compliance and predict heating and cooling loads.
PCB thermal vias: Copper-filled vias through a printed circuit board act as high-conductivity columns (k ≈ 385 W/m·K) that conduct heat from a surface-mount component on one side to a copper plane or heatsink on the other, dramatically reducing thermal resistance compared with the surrounding FR4 laminate (k ≈ 0.3 W/m·K).

Frequently Asked Questions

Why is my heat flow higher than expected? The most common causes are parallel heat paths and contact resistance. If studs, fasteners, or brackets bridge an insulated assembly, they conduct heat in parallel with the insulation and raise the effective conductance significantly. Contact resistance in the opposite direction can sometimes cause measured heat flow to be lower than predicted when surfaces are poorly mated and the gap acts as an additional insulating layer.

When does Fourier's law break down? At the nanoscale, when the mean free path of heat-carrying phonons approaches the film thickness, the classical diffusion model no longer applies and ballistic phonon transport must be considered. This matters for thin-film semiconductor devices and nanoscale heat spreaders. At very high temperatures, radiation from a hot surface can carry more energy than conduction through the adjacent solid, making the assumption that Q = k·A·ΔT/L a significant underestimate of total heat transfer.