LMTD and correction factor F
Log mean temperature difference, the P/R parameters and the F correction factor for shell-and-tube exchangers.
Process data
FLUIDO CALIENTE
COLD FLUID
Default example: thermal oil cooled from 180 to 120 with cooling-tower water from 30 to 45.
Results
ΔT₁
—
ΔT₂
—
P
—
R
—
LMTD
—
Factor F
—
ΔTm = F·LMTD
—
Interactive thermal profile
Normalised position along the exchanger (0 = reference inlet, 1 = outlet). For 1–2 and 2–4 arrangements, the equivalent countercurrent approximation used for the LMTD calculation is shown.
Calculation report as PDF
Generates an engineering datasheet with the energy balance, LMTD, U, area A and the thermal profile.
Theory guide: heat exchanger calculations
The preliminary design of a heat exchanger follows a logical calculation sequence that can be solved with the log mean temperature difference (LMTD). First the mean temperature difference between the hot and cold streams along the equipment is determined; in arrangements that are not purely countercurrent or cocurrent — such as multi-pass shell-and-tube exchangers — that log mean must be corrected by a dimensionless factor F, which depends on the P and R ratios between the process temperatures.
Once the corrected mean temperature is known, the second step is to estimate the overall heat transfer coefficient U, which groups in series the thermal resistances of the inside film, the fouling on both sides, the metal tube wall and the outside film. That coefficient, together with the heat duty Q from the energy balance, allows the required transfer area and, from it, to estimate the number of tubes required for a standard bundle length.
For phenomena where time matters — such as heating or cooling a solid — the analysis moves from steady state to transient conduction. The Biot and Fourier numbers decide whether a lumped-capacitance model (uniform temperature throughout the solid) is sufficient, or whether the one-term Heisler solutions are needed, which are valid once the Fourier number is high enough. Finally, in insulated pipes and conductors, the concept of critical insulation radius explains why, in small-diameter geometries, adding a thin layer of insulation can paradoxically increase heat loss before it starts to reduce it.
Methodology based on the heat transfer fundamentals of McCabe, Smith and Harriott — Unit Operations of Chemical Engineering.
Preguntas frecuentes
What is the difference between the LMTD method and the NTU-effectiveness method?
The LMTD method is direct when all four inlet and outlet temperatures are known, and is typically used to size a new exchanger (computing the area from Q, U and ΔTm). The NTU-effectiveness method is preferable when not all outlet temperatures are known — for example when rating an existing exchanger — because it states the problem in terms of thermal effectiveness and the number of transfer units, with no iteration required.
When must the F correction factor be applied?
The F factor is needed whenever the flow arrangement is not purely countercurrent or cocurrent, as in single- or multi-pass shell-and-tube exchangers or in cross-flow exchangers. In pure countercurrent or cocurrent flow, F = 1 and the calculated LMTD already represents the true mean temperature difference.
Why is a design considered unworkable when F falls below 0.75?
A low F factor means the chosen arrangement departs far from ideal countercurrent behaviour, which forces a disproportionately large transfer area to achieve the same heat exchange. As a rule of thumb, keep F above 0.75; lower values usually indicate that the number of shell passes should be increased or the configuration reconsidered.
What does the Biot number mean physically?
The Biot number compares the resistance to conduction inside a solid with the resistance to convection at its surface. A very small Biot number (below 0.1) means the solid conducts heat far more easily than the fluid can remove or supply it, so the internal temperature stays practically uniform at all times — the condition that justifies the simplified lumped-capacitance model.
Why can adding insulation to a thin cable increase heat loss?
In a cylindrical geometry, adding insulation simultaneously increases the conduction resistance and the surface area available for convection. When the original radius is smaller than the critical radius (kins/ho), the effect of the larger convection area initially dominates over the added resistance, and heat loss rises until the outer radius exceeds the critical radius; beyond that point, each additional layer does reduce the heat loss.
How accurate is the one-term Heisler model compared with the exact solution?
The one-term approximation converges quickly to the full series solution as the Fourier number grows, and is generally considered accurate enough (error below 2%) for Fo > 0.2. At shorter times the higher-order terms of the series are still significant, and this calculator warns the user when a result falls outside that range of validity.