Math & Numbers

Overall Heat Transfer Coefficient (1/U=ΣR)

Compute the overall heat transfer coefficient for series thermal resistances (flat-wall model): total resistance R_total = Σ R_i (K/W), thermal conductance G = 1/R_total (W/K), area-based coefficient U = 1/(R_total·A) (W/(m²·K)), and if a temperature difference is given the heat flow rate Q = ΔT/R_total (W). Each R_i is a layer resistance already containing the area factor (e.g. convection R_conv=1/(h·A), conduction R_cond=d/(k·A), fouling R_foul=R_f''/A). Enter one resistance (K/W) per line, at least one, all positive. ΔT may be negative (reverse heat flow); a °C difference equals a K difference, a °F difference is converted by ×5/9.

json· JSON resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'http://127.0.0.1:3003/en/api/tools/overall-heat-transfer-coefficient' \
  -H 'Content-Type: application/json' \
  -d '{"resistances":"0.02\n0.5\n0.01","area":1,"temperatureDiff":0,"tempUnit":"K","decimalPlaces":4}'

API reference

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

Endpoint

HTTP

POST http://127.0.0.1:3003/en/api/tools/overall-heat-transfer-coefficient

Parameters

Name	Type	Required	Description
resistances	textarea	Yes	One thermal resistance per line (K/W), already containing the area factor (e.g. R_conv=1/(h·A), R_cond=d/(k·A), R_foul=R_f''/A). At least one positive value required.
area	number	No	Heat transfer area A (m²) used to collapse R_total to the area-based overall coefficient U = 1/(R_total·A). Must be positive.
temperatureDiff	number	No	Temperature difference ΔT across the resistance stack, in the selected Temperature Unit. If provided, the heat flow rate Q = ΔT/R_total is computed. 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.

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-overall-heat-transfer-coefficient": {
      "name": "overall-heat-transfer-coefficient",
      "description": "Compute the overall heat transfer coefficient for series thermal resistances (flat-wall model): total resistance R_total = Σ R_i (K/W), thermal conductance G = 1/R_total (W/K), area-based coefficient U = 1/(R_total·A) (W/(m²·K)), and if a temperature difference is given the heat flow rate Q = ΔT/R_total (W). Each R_i is a layer resistance already containing the area factor (e.g. convection R_conv=1/(h·A), conduction R_cond=d/(k·A), fouling R_foul=R_f''/A). Enter one resistance (K/W) per line, at least one, all positive. ΔT may be negative (reverse heat flow); a °C difference equals a K difference, a °F difference is converted by ×5/9.",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=overall-heat-transfer-coefficient",
      "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": "overall-heat-transfer-coefficient",
    "arguments": {
  "resistances": "0.02\n0.5\n0.01",
  "area": 1,
  "temperatureDiff": 0,
  "tempUnit": "K",
  "decimalPlaces": 4
}
  }
}

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