Math & Numbers

Heat Exchanger ε-NTU Calculator (Effectiveness-NTU Method)

Compute the effectiveness (ε) of a heat exchanger by the ε-NTU method. C*=C_min/C_max (0..1), NTU=U·A/C_min, q_max=C_min·(T_h,in-T_c,in), and ε=q_actual/q_max. Supports four arrangements: Parallel flow ε=[1-exp(-NTU(1+C*))]/(1+C*); Counter flow ε=[1-exp(-NTU(1-C*))]/[1-C*·exp(-NTU(1-C*))], or NTU/(1+NTU) when C*=1; Shell-and-tube 1-2 ε=2/[1+C*+√(1+C*²)·(1+exp(-NTU√(1+C*²)))/(1-exp(-NTU√(1+C*²)))]; Crossflow (both unmixed) ε=1-exp{(NTU^0.22/C*)·[exp(-C*·NTU^0.78)-1]}. When C*=0 (phase change on one side, boiler/condenser) every arrangement gives ε=1-exp(-NTU). Optionally supply T_h,in and T_c,in to recover the actual heat-transfer rate q=ε·q_max and both outlet temperatures. Temperatures are used only as differences: Δ°C=ΔK and Δ°F×5/9=ΔK.

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-exchanger-ntu' \
  -H 'Content-Type: application/json' \
  -d '{"exchangerType":"counter","hotCapacityRate":1000,"coldCapacityRate":1500,"overallU":500,"area":10,"hotInletTemp":0,"coldInletTemp":0,"tempUnit":"°C","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-exchanger-ntu

Parameters

Name	Type	Required	Description
exchangerType	select	No	Exchanger arrangement: Parallel Flow, Counter Flow, Shell-and-Tube (1 shell pass / 2 tube passes), or Crossflow (single pass, both fluids unmixed).
hotCapacityRate	number	Yes	Hot-side heat-capacity rate C_h = ṁ_h·c_p,h in W/K.
coldCapacityRate	number	Yes	Cold-side heat-capacity rate C_c = ṁ_c·c_p,c in W/K.
overallU	number	Yes	Overall heat transfer coefficient U in W/(m²·K).
area	number

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-exchanger-ntu": {
      "name": "heat-exchanger-ntu",
      "description": "Compute the effectiveness (ε) of a heat exchanger by the ε-NTU method. C*=C_min/C_max (0..1), NTU=U·A/C_min, q_max=C_min·(T_h,in-T_c,in), and ε=q_actual/q_max. Supports four arrangements: Parallel flow ε=[1-exp(-NTU(1+C*))]/(1+C*); Counter flow ε=[1-exp(-NTU(1-C*))]/[1-C*·exp(-NTU(1-C*))], or NTU/(1+NTU) when C*=1; Shell-and-tube 1-2 ε=2/[1+C*+√(1+C*²)·(1+exp(-NTU√(1+C*²)))/(1-exp(-NTU√(1+C*²)))]; Crossflow (both unmixed) ε=1-exp{(NTU^0.22/C*)·[exp(-C*·NTU^0.78)-1]}. When C*=0 (phase change on one side, boiler/condenser) every arrangement gives ε=1-exp(-NTU). Optionally supply T_h,in and T_c,in to recover the actual heat-transfer rate q=ε·q_max and both outlet temperatures. Temperatures are used only as differences: Δ°C=ΔK and Δ°F×5/9=ΔK.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=heat-exchanger-ntu",
      "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-exchanger-ntu",
    "arguments": {
  "exchangerType": "counter",
  "hotCapacityRate": 1000,
  "coldCapacityRate": 1500,
  "overallU": 500,
  "area": 10,
  "hotInletTemp": 0,
  "coldInletTemp": 0,
  "tempUnit": "°C",
  "decimalPlaces": 4
}
  }
}

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