Heat Conduction Calculator (Fourier's Law, q=kΔT/d)

Heat Conduction Calculator (Fourier's Law, q=kΔT/d) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

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.

conductivity: 0.04; temperatureDiff: 20; tempUnit: K; thickness: 0.05; thicknessUnit: m; crossSectionArea: 1; areaUnit: m2; decimalPlaces: 4

Outcome

The calculator returns q = 16 W/m², Q = 16 W, and R = 1.25 K/W.

2. Steel plate heat transfer

Mechanical engineering student

Background

A student is analyzing a 2 cm steel plate with a 100 °C temperature difference across a 500 cm² section.

Problem

Calculate the large heat flux and total heat flow through the conductive plate.

How to use

Enter k = 50 W/(m·K), ΔT = 100 °C, thickness = 2 cm, and area = 500 cm².

FAQ

What does this heat conduction calculator calculate?

It calculates heat flux q, heat flow rate Q, and thermal resistance R for one-dimensional steady conduction through a flat slab.

Which inputs are required?

Thermal conductivity, temperature difference, and slab thickness are required. Cross-sectional area defaults to 1 m² if left unchanged.

Can the temperature difference be negative?

Yes. A negative ΔT indicates heat flow in the reverse direction.

What units are supported?

Temperature differences can be entered in K, °C, or °F; thickness in m, cm, or mm; and area in m² or cm².

What values must be positive?

Thermal conductivity, thickness, and cross-sectional area must be positive. The temperature difference may be negative.

conductivity: 50; temperatureDiff: 100; tempUnit: °C; thickness: 2; thicknessUnit: cm; crossSectionArea: 500; areaUnit: cm2; decimalPlaces: 4

Run this tool

Examples that match this tool

Continue with connected tools and hubs

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Glass wool insulation wall

2. Steel plate heat transfer

FAQ

Web Image Processing Python Samples

Android Image Processing Java Samples

Android Image Processing Kotlin Samples

Web Image Processing Rust Samples

Absolute Value Calculator

Air Changes per Hour (ACH, n = Q/V)

Bearing Life L10 Calculator

Bolt Torque Clamp Force Calculator