Calculator Inputs
Use shell-and-tube temperatures for the selected duty. Flow and heat capacity inputs are optional, but they enable heat-duty checks and area estimates.
Example Data Table
| Case | Th,in | Th,out | Tc,in | Tc,out | Shell Passes | R | P | Ft | Corrected LMTD | Duty Estimate |
|---|---|---|---|---|---|---|---|---|---|---|
| Reference exchanger | 180 | 120 | 40 | 90 | 1 | 1.2000 | 0.3571 | 0.9262 | 78.6398 °C | 412.859 kW |
This example assumes U = 350 W/m²·K and area = 15 m². It also uses balanced stream duties from the default values above.
Formulas Used
R = (Th,in - Th,out) / (Tc,out - Tc,in)P = (Tc,out - Tc,in) / (Th,in - Tc,in)
ΔT1 = Th,in - Tc,outΔT2 = Th,out - Tc,inLMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
S = √(R² + 1) / (R - 1)W = ((1 - P·R) / (1 - P))1/NFt = [S ln(W)] / ln[(1 + W - S + SW) / (1 + W + S - SW)]
ΔTcorr = Ft × LMTDQ = U × A × ΔTcorrQ = ṁ × Cp × ΔT
The correction factor expression is commonly used for shell-and-tube arrangements with multiple shell passes. Very low Ft values often signal an arrangement that deserves redesign review.
How to Use This Calculator
- Enter the hot-side inlet and outlet temperatures.
- Enter the cold-side inlet and outlet temperatures.
- Specify the number of shell passes for the exchanger.
- Optionally enter U, area, target duty, mass flow rates, and heat capacities.
- Press Calculate to display results above the form.
- Review Ft, corrected LMTD, duty checks, and the Plotly curve.
- Use the CSV or PDF buttons to save the result snapshot.
- If Ft is low, compare alternate temperature programs or pass arrangements.
Frequently Asked Questions
1) What does the LMTD correction factor represent?
It adjusts the ideal counterflow LMTD so it matches the real exchanger flow arrangement. Complex shell-and-tube paths reduce the true average driving force, so Ft usually stays below 1.
2) Why are R and P important?
R captures the relative temperature changes of the two streams. P measures how much the cold stream heats relative to the maximum possible rise. Together they determine Ft.
3) What Ft value is usually considered acceptable?
Many designers prefer Ft above 0.75 for practical performance. Lower values can still occur, but they often suggest the selected pass arrangement or outlet targets deserve another look.
4) Can I use Celsius or Kelvin?
Yes. Because the equations use temperature differences, Celsius and Kelvin give identical results as long as every entered temperature uses the same scale.
5) Why does the calculator reject some inputs?
Some temperature combinations create nonphysical log terms or impossible exchanger behavior. Examples include negative terminal differences, reversed heating trends, or combinations where the correction factor expression becomes undefined.
6) What is the difference between counterflow LMTD and corrected LMTD?
Counterflow LMTD assumes an ideal countercurrent path. Corrected LMTD multiplies that value by Ft so the result better represents the real shell-and-tube temperature driving force.
7) Why include mass flow and heat capacity fields?
Those optional fields let you compare thermal duty from stream data with duty from U·A·ΔTcorr. That makes it easier to spot energy imbalance or sizing mismatches.
8) Can this help estimate exchanger area?
Yes. When you enter U and either a target duty or stream duty, the calculator estimates the area needed to achieve that performance using the corrected temperature driving force.