Math & Numbers
Cylinder Radial Heat Conduction (Q=2πkL·ΔT/ln(r₂/r₁))
Compute radial steady-state heat conduction through a single-layer cylindrical wall (Fourier's law in cylindrical coordinates): radial heat flow rate Q = 2π·k·L·ΔT/ln(r₂/r₁) (W), inner-surface heat flux q_inner = Q/(2π·r₁·L) (W/m²), outer-surface heat flux q_outer = Q/(2π·r₂·L) (W/m²), and cylindrical thermal resistance R = ln(r₂/r₁)/(2π·k·L) (K/W). k is the thermal conductivity (W/(m·K)); L the cylinder length; r₁ the inner radius, r₂ the outer radius (must have r₂ > r₁ > 0); ΔT the temperature difference (K; a °C difference equals a K difference, a °F difference is converted by ×5/9). ΔT may be negative (indicating reverse heat flow), but k, L, r₁ and r₂ must be positive. Length and radius in m/cm/mm.
Quick start
Call this tool from your code in three languages.
curl -X POST 'https://api.elysiatools.com/en/api/tools/cylinder-radial-conduction' \
-H 'Content-Type: application/json' \
-d '{"conductivity":50,"length":2,"lengthUnit":"m","innerRadius":0.05,"outerRadius":0.1,"radiusUnit":"m","temperatureDiff":100,"tempUnit":"K","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/cylinder-radial-conductionParameters
| Name | Type | Required | Description |
|---|---|---|---|
| conductivity | number | Yes | Thermal conductivity k of the cylinder-wall material in W/(m·K). |
| length | number | Yes | Cylinder length L, in the selected Length Unit. |
| lengthUnit | select | No | — |
| innerRadius | number | Yes | Inner radius r₁ of the cylinder wall, in the selected Radius Unit. |
| outerRadius | number | Yes |
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-cylinder-radial-conduction": {
"name": "cylinder-radial-conduction",
"description": "Compute radial steady-state heat conduction through a single-layer cylindrical wall (Fourier's law in cylindrical coordinates): radial heat flow rate Q = 2π·k·L·ΔT/ln(r₂/r₁) (W), inner-surface heat flux q_inner = Q/(2π·r₁·L) (W/m²), outer-surface heat flux q_outer = Q/(2π·r₂·L) (W/m²), and cylindrical thermal resistance R = ln(r₂/r₁)/(2π·k·L) (K/W). k is the thermal conductivity (W/(m·K)); L the cylinder length; r₁ the inner radius, r₂ the outer radius (must have r₂ > r₁ > 0); ΔT the temperature difference (K; a °C difference equals a K difference, a °F difference is converted by ×5/9). ΔT may be negative (indicating reverse heat flow), but k, L, r₁ and r₂ must be positive. Length and radius in m/cm/mm.",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=cylinder-radial-conduction",
"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": "cylinder-radial-conduction",
"arguments": {
"conductivity": 50,
"length": 2,
"lengthUnit": "m",
"innerRadius": 0.05,
"outerRadius": 0.1,
"radiusUnit": "m",
"temperatureDiff": 100,
"tempUnit": "K",
"decimalPlaces": 4
}
}
}