Heat Conduction Calculator (Fourier Law)
Calculate heat flux, total heat flow, and thermal resistance through a wall or slab using Fourier's Law of heat conduction.
Enter conductivity, thickness, area, and temperature difference.
Fourier’s Law of Heat Conduction Heat conduction is the transfer of thermal energy through a material due to a temperature gradient. Jean-Baptiste Joseph Fourier established the fundamental law governing this process in 1822: heat flows from hot to cold, and the rate of flow is proportional to the temperature gradient and the material’s thermal conductivity.
Heat Flux Formula Heat flux q (power per unit area) is calculated as:
q = k x DeltaT / L (W/m²)
Where:
- k = thermal conductivity of the material (W/m·K)
- DeltaT = temperature difference across the wall (K or °C, same numerically)
- L = thickness of the wall or slab (m)
Total Heat Flow Rate Multiplying heat flux by the surface area gives the total power conducted:
Q = q x A = k x A x DeltaT / L (Watts)
This is the steady-state heat transfer rate — the energy flowing per second through the entire surface.
Thermal Resistance (R-Value) Thermal resistance R measures how much a material resists heat flow. It is the inverse of conductance:
R = L / k (m²·K/W)
A higher R-value means better insulation. In building science, R-values are often expressed in imperial units (ft²·°F·h/BTU), but the SI definition above is the engineering standard.
Common Thermal Conductivity Values Copper: ~385 W/m·K (excellent conductor) Aluminum: ~205 W/m·K Steel: ~50 W/m·K Concrete: ~1.7 W/m·K Glass: ~1.0 W/m·K Brick: ~0.6-0.8 W/m·K Wood (pine): ~0.12 W/m·K Mineral wool insulation: ~0.04 W/m·K Still air: ~0.026 W/m·K (excellent insulator)
Steady-State vs. Transient Fourier’s Law as applied here describes steady-state conduction — where temperatures do not change with time. Transient analysis (heating and cooling over time) requires solving the heat equation and is significantly more complex.
Applications Heat conduction calculations are essential in building insulation design, heat exchanger engineering, electronic cooling, pipe insulation, furnace wall design, and any application where controlling heat flow is critical to performance or energy efficiency.
Composite Walls For walls made of multiple layers, thermal resistances add in series: R_total = R1 + R2 + R3 = L1/k1 + L2/k2 + L3/k3 Total heat flux = DeltaT / R_total