Math & Numbers

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

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.

json· JSON resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/heat-conduction-calculator' \
  -H 'Content-Type: application/json' \
  -d '{"conductivity":0.04,"temperatureDiff":20,"tempUnit":"K","thickness":0.05,"thicknessUnit":"m","crossSectionArea":1,"areaUnit":"m2","decimalPlaces":4}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/heat-conduction-calculator

Parameters

Name	Type	Required	Description
conductivity	number	Yes	Thermal conductivity k of the slab material in W/(m·K).
temperatureDiff	number	Yes	Temperature difference ΔT across the slab, in the selected Temperature Unit. May be negative to indicate the reverse heat-flow direction.
tempUnit	select	No	Unit of the temperature difference. This is a difference, not an absolute temperature: Δ°C = ΔK and Δ°F ×5/9 = ΔK.
thickness	number	Yes	Slab thickness d, in the selected Thickness Unit.
thicknessUnit

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-heat-conduction-calculator": {
      "name": "heat-conduction-calculator",
      "description": "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.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=heat-conduction-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "heat-conduction-calculator",
    "arguments": {
  "conductivity": 0.04,
  "temperatureDiff": 20,
  "tempUnit": "K",
  "thickness": 0.05,
  "thicknessUnit": "m",
  "crossSectionArea": 1,
  "areaUnit": "m2",
  "decimalPlaces": 4
}
  }
}

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