NTU-Effectiveness Heat Exchanger Calculator mechanism

Model scope

The NTU and capacity-ratio definitions and the supplied counterflow correlation are standard under the stated assumptions. The specification needs explicit inlet-temperature inputs, outlet equations, a complete configuration-to-correlation mapping, the Cr=1 limit, unit validation, and positive-capacity constraints before it can be labeled as a complete calculator.

• NTU=UA/Cmin is standard when U is an overall heat-transfer coefficient in W/(m²·K), A is in m², and Cmin is in W/K.
• Cr=Cmin/Cmax is standard, but Cmin and Cmax must be computed as m_dot·cp using consistent units.
• The counterflow effectiveness formula is correct for Cr≠1: ε=(1−exp(−NTU·(1−Cr)))/(1−Cr·exp(−NTU·(1−Cr))).
• For counterflow Cr=1, the displayed formula becomes 0/0 and must be replaced by its limiting form ε=NTU/(1+NTU).
• Configuration-specific correlations are not provided for parallel flow, crossflow, multipass, or other configurations; the calculator cannot safely accept a generic configuration without those formulas.
• Outlet temperatures require inlet hot and cold temperatures, which are absent from the declared inputs.

Units and conventions

• U is in W/(m²·K).
• A is in m².
• Mass flow rates are in kg/s.
• Specific heat capacities are in J/(kg·K), so each capacity rate C=m_dot·cp is in W/K.
• Temperatures used in temperature differences may be in °C or K; absolute temperatures are not needed for these formulas, but both inlet temperatures must use the same scale.
• q is reported in W and outlet temperatures in °C in the test vectors.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "configuration": "counterflow",
    "U_W_m2K": 500,
    "A_m2": 10,
    "m_hot_kg_s": 0.5,
    "cp_hot_J_kgK": 4180,
    "m_cold_kg_s": 0.8,
    "cp_cold_J_kgK": 4180,
    "T_hot_in_C": 180,
    "T_cold_in_C": 20
  },
  "expected_outputs": {
    "epsilon": 0.7948075,
    "q_W": 132891.81,
    "T_hot_out_C": 116.4154,
    "T_cold_out_C": 59.7404
  },
  "working": "Ch=0.5·4180=2090 W/K; Cc=0.8·4180=3344 W/K; Cmin=2090; Cmax=3344; Cr=2090/3344=0.625. UA=500·10=5000 W/K. NTU=5000/2090=2.3923445. x=NTU·(1−Cr)=2.3923445·0.375=0.8971292. exp(−x)=exp(−0.8971292)=0.4077385. ε=(1−0.4077385)/(1−0.625·0.4077385)=0.5922615/0.7451634=0.7948075. ΔTin=180−20=160 K. q=0.7948075·2090·160=132891.81 W. Th,out=180−132891.81/2090=180−63.5846=116.4154 °C. Tc,out=20+132891.81/3344=20+39.7404=59.7404 °C."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The raw counterflow formula is undefined at Cr=1 because it becomes 0/0, requiring the limiting expression epsilon=NTU/(1+NTU). A zero capacity rate makes NTU divide by zero and should be rejected. These are concrete failure points unless explicit boundary and input validation branches are implemented.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json