What this calculator does

This conduction heat transfer calculator estimates one-dimensional steady heat flow through a material layer using Fourier's law. It is a practical tool for quick wall, slab, panel, and insulation estimates when you know conductivity, area, thickness, and temperature difference.

Conduction is one of the core ways heat moves through solids. If one side of a material is hotter than the other, energy flows from hot to cold. The rate depends on how conductive the material is, how much area participates, how thick the path is, and how large the temperature difference is.

Inputs explained

• Thermal conductivity k: Enter the material conductivity in W/(m K) or the unit expected by the page.
• Area A: Enter the heat-transfer area normal to the conduction path.
• Thickness L: Enter the distance heat must travel through the material.
• Temperatures: Enter the hot-side and cold-side temperatures so the page can compute delta T.

How it works / method

The page applies the simplest steady one-dimensional conduction relationship. It computes the temperature difference between the two sides and then scales that difference by conductivity and area, divided by thickness. The result is a heat-transfer rate and a heat-flux value so you can compare both total transfer and transfer per unit area.

Formula used

This is Fourier's law in a very simplified steady-state form. It assumes a uniform layer, constant material conductivity, one-dimensional flow, and no thermal contact resistance or internal heat generation.

Step-by-step example

Suppose a panel has k = 0.04 W/(m K), area = 10 m^2, thickness = 0.1 m, a hot-side temperature of 30 C, and a cold-side temperature of 10 C.

1. Enter 0.04 for thermal conductivity.
2. Enter 10 for area and 0.1 for thickness.
3. Enter 30 for the hot side and 10 for the cold side so delta T is 20 C.
4. The calculator estimates the steady conduction heat-transfer rate through the panel.
5. If thickness doubles, the heat-transfer rate is roughly cut in half under the same assumptions.

Use cases

• Quick insulation sanity checks for walls, roofs, coolers, and enclosures.
• Comparing candidate materials with different conductivity values.
• Teaching the direct proportionalities in Fourier's law.
• Estimating heat-transfer rates before moving into layered or transient models.

Assumptions and limitations

• The page assumes steady one-dimensional conduction and a single effective conductivity value.
• It does not model radiation, convection, thermal bridges, moisture migration, or contact resistance.
• Thermal conductivity can vary with temperature and material orientation, which this compact tool does not resolve.
• Units must be consistent. Incorrect area, thickness, or conductivity units will produce misleading outputs.

Use this calculator for quick estimates and screening. For multilayer assemblies, transient heating, or real construction details, a more complete thermal model is appropriate.

Sources & references

• NASA Glenn - Heat transfer fundamentals
• NASA Glenn - Specific heat capacity
• NASA Glenn - Earth atmosphere equation
• NASA Glenn - Air pressure fundamentals
• NIST Chemistry WebBook - Water phase change data
• NIST WTT-Pro - Boiling point from vapor pressure
• NIST - Fused quartz thermal expansion reference
• NIST - Example thermal conductivity tables