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.
Quick start
Call this tool from your code in three languages.
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
POST https://api.elysiatools.com/en/api/tools/heat-conduction-calculatorParameters
| 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:
{
"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:
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Call this tool
Invoke the tool by its id, passing arguments built from its parameters:
{
"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
}
}
}