Compute 1-D steady-state heat conduction through a flat slab (Fourier's law): heat flux q = k·ΔT/d (W/m²), heat flow rate Q = k·A·ΔT/d (W), and thermal resistance R = d/(k·A) (K/W). k is the thermal conductivity (W/(m·K)); ΔT is the temperature difference (K; a °C difference equals a K difference, a °F difference is converted by ×5/9); d the slab thickness; A the cross-section area. ΔT may be negative (indicating reverse heat flow), but k, d and A must be positive. Thickness in m/cm/mm, area in m²/cm².
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Key facts
Category
Math & Numbers
Input types
number, select
Output type
json
Sample coverage
4
API ready
Yes
Overview
Calculate steady-state one-dimensional heat conduction through a flat slab using Fourier’s law. Enter thermal conductivity, temperature difference, thickness, and cross-sectional area to get heat flux, heat flow rate, and thermal resistance.
When to use
Estimate heat transfer through an insulation layer, wall, or flat plate.
Compare thermal resistance for different slab thicknesses or materials.
Calculate heat flux and total heat flow when the temperature difference and area are known.
How it works
1Enter thermal conductivity k in W/(m·K), temperature difference ΔT, slab thickness d, and cross-sectional area A.
2Select the temperature, thickness, and area units; temperature differences in °C equal the same difference in K, while °F differences are converted by multiplying by 5/9.
3The calculator applies q = k·ΔT/d, Q = k·A·ΔT/d, and R = d/(k·A).
4The JSON result reports heat flux in W/m², heat flow rate in W, and thermal resistance in K/W.
Use cases
Evaluate glass wool or other insulation layers for wall heat-loss estimates.
Calculate heat transfer through metal plates and structural wall sections.
Use thermal resistance to compare slab designs with different materials, areas, or thicknesses.
Examples
1. Glass wool insulation wall
Building engineer
Background
An engineer wants to estimate steady heat transfer through a 5 cm glass wool slab separating spaces with a 20 K temperature difference.
Problem
Find the heat flux, total heat flow, and thermal resistance for a 1 m² insulation section.
How to use
Enter k = 0.04 W/(m·K), ΔT = 20 K, thickness = 0.05 m, and area = 1 m².