A reported cooler approach temperature is ambiguous until its two measuring points are named. For a counterflow model, the DOE heat-transfer handbook defines the two opposite-end temperature differences used in LMTD [1]. One end difference alone is not the mean driving force.
Label oil inlet Toi, oil outlet Too, water inlet Twi and water outlet Two. Temperatures may be in °C because their differences are kelvin. Record whether the cooler is counterflow, parallel flow or a multipass arrangement.
For ideal counterflow, pair opposite ends
Define ΔT1 = Toi − Two and ΔT2 = Too − Twi. For positive end differences, ΔTlm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2). When the two differences coincide, use their limiting common value. A different flow arrangement needs its appropriate pairing and correction.
| Reported quantity | Named points | Interpretation |
|---|---|---|
| Inlet temperature difference | Toi − Twi | Thermal boundary, not mean driving force |
| Counterflow outlet approach | Too − Twi | Oil outlet proximity to cold inlet |
| Oil cooling range | Toi − Too | Needs oil flow to calculate heat duty |
| Water rise | Two − Twi | Needs water flow to calculate heat duty |
A manufacturer instruction manual illustrates placing thermometer and pressure connections close to the exchanger [2]. On the installed oil circuit, locate each sensor relative to the cooler and any bypass mixing junction.
Compute the counterflow end differences
Assume steady oil temperatures of 70 °C inlet and 50 °C outlet, and water temperatures of 30 °C inlet and 40 °C outlet. Counterflow end differences are 30 K and 20 K, giving LMTD 24.66 K. Oil-outlet approach is 20 K, a different quantity. Use the correct flow arrangement and matched heat balance before deriving UA.
For an additional assumed matched duty of 100 kW, using the 20 K outlet approach would give UA = 5.00 kW/K; using LMTD gives 4.055 kW/K. The incorrect denominator overstates UA by 23.32%. Check duty agreement on both fluids before assigning degradation to U.
Check the measuring points before interpreting the value
A sensor downstream of a bypass mixing point measures mixed oil, not the cooler outlet alone. A water sensor far along an exposed pipe may include ambient heat exchange. Place each reading on the system diagram.
References
- U.S. Department of Energy, DOE-HDBK-1012/2-92, Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2, 1992.
- Alfa Laval, Pharma-line Instruction Manual, ESE02198-EN, May 2012, sections 1.4, 2.5, 4.2 and 4.4.