LMTD Calculator and Heat Exchanger Sizing

Log mean temperature difference is the correct average driving force between two streams along an exchanger. It is logarithmic because the temperature difference does not change linearly down the length: heat transfer is fastest where the streams are furthest apart, so the gap closes quickly at first and slowly afterwards. Using a simple arithmetic average of the two end differences always overstates the driving force.

Take the temperature difference at each end of the exchanger, subtract them, and divide by the natural log of their ratio. For clean steam at 250°F heating WFI from 70 to 175°F, the end differences are 75 and 180°F, giving an LMTD of about 118°F. If the two end differences are equal, the log form is undefined and the LMTD is simply that value.

In counterflow the streams run in opposite directions, which keeps the temperature difference more even along the length and produces a higher LMTD for the same terminal temperatures. Parallel flow starts with a huge difference that collapses quickly. Counterflow is more effective for the same area, which is why it is the default arrangement, and it is also the only arrangement that can bring the cold outlet above the hot outlet.

The LMTD equation assumes true counterflow. Real shell-and-tube and plate exchangers have multiple passes and mixed flow directions, so the effective driving force is lower. The F factor corrects for that geometry and is always one or less. Designs where F falls much below about 0.8 are usually reconsidered, because the arrangement is fighting itself and small temperature errors produce large area errors.

Because U is a series of resistances: the two film coefficients, the wall, and the fouling on both sides. The fouling allowance is an estimate of the future, and it commonly dominates. Published U ranges are broad for that reason, and a sizing done at the optimistic end of a range produces an exchanger that works on commissioning day and fails to hold duty a year later.

The same equation applies but the situation is different, because a batch in a jacketed vessel is not at steady state. The batch temperature rises as it heats, so the driving force shrinks continuously and the calculation becomes a time-dependent one. Steady-state LMTD gives a useful instantaneous answer at a chosen batch temperature, not a heat-up time.

It sets the margin. A clean exchanger meeting duty exactly has no reserve, and on a hygienic water system the first rouge or scale layer takes it below duty. Specifying a fouling allowance appropriate to the service, rather than sizing on clean coefficients, is what keeps the unit meeting duty between cleanings rather than only when new.

Because saturated steam condenses at constant temperature, so the hot side has no temperature change at all. Both end differences are measured from the same steam temperature, which makes the LMTD straightforward and the duty easy to control by varying steam pressure. The temperature that goes into the calculation comes straight off a steam table.

Number of Transfer Units relates the exchanger’s size to the heat capacity of the streams and yields an effectiveness, the fraction of the theoretically possible heat actually transferred. It is preferred when the outlet temperatures are unknown, because LMTD requires them as inputs. Rating an existing exchanger on a new duty is the classic NTU problem; sizing a new one for known temperatures is the classic LMTD problem.

The gap between the outlet of one stream and the inlet of the other, and it is what drives cost. A tight approach demands a large area because the driving force in that region is small, and the area needed rises steeply as the approach closes. Specifying an unnecessarily tight approach is one of the commonest ways to make an exchanger expensive.

The location along the exchanger where the temperature difference is at its minimum. It sets the limit on how much heat can be recovered, and it does not always sit at an end of the unit — with a phase change or a varying specific heat it can appear in the middle, which a simple end-to-end LMTD calculation will not reveal.

A plate exchanger gives far more area in a given volume, achieves closer approaches, and can be opened and extended. A shell and tube handles higher pressures and temperatures, tolerates fouling better and is more robust. Hygienic duties frequently use plate or specialised tubular designs because they can be cleaned and inspected.

A construction with two separated tube sheets and a vented gap between them, so a leak at either tube-to-tubesheet joint escapes to atmosphere rather than crossing between the two fluids. It is specified where cross-contamination is unacceptable, for example between plant steam or cooling water and WFI, and the vented gap makes a leak visible.

Because the resistances add in series and a thin fouling layer has very low conductivity. Once the film coefficients on both sides are reasonably good, they stop being the limiting term and the fouling allowance becomes the largest single resistance. That is why published U ranges are wide and why the fouling assumption deserves more scrutiny than the film calculations.

One appropriate to the service and the cleaning interval, taken from published guidance for that fluid rather than from a default. On high-purity water the relevant mechanism is usually rouge or scale rather than classic process fouling, and the cleaning regime is what keeps it in check. An exchanger sized on clean coefficients has no margin at all.

In place where the design permits, using the same CIP chemistry and velocity rules as the rest of the loop, which requires the exchanger to be drainable and free of dead zones. Plate units can also be opened and mechanically cleaned. Any exchanger on a hygienic service has to be evaluated as part of the cleaning circuit, not as a separate item.

Because a flooded surface transfers heat far less effectively than a condensing one. When condensate cannot drain, it blankets the lower part of the surface and the effective area falls, so the exchanger cannot hold setpoint even though the steam supply is correct. It is regularly misdiagnosed as an undersized unit.

The condition where the control valve has throttled the steam pressure so far that it can no longer push condensate through the trap against the downstream return pressure. The exchanger floods at part load, control becomes erratic, and the fix is a pumping trap or a vented arrangement rather than a larger exchanger.

Usually the steam side, because varying the steam pressure moves the condensing temperature directly along the saturation curve and gives a responsive, near-isothermal control. The consequence is the stall condition above, which is why the condensate removal arrangement has to be designed alongside the control scheme.

Because at normal load the control valve has to sit almost closed to avoid overshooting, which is exactly where its authority and resolution are worst. The loop hunts, and at low demand a steam-heated unit is also more likely to stall. An exchanger with excessive margin controls worse than one correctly sized.

BTU per hour in the units used here, or watts in SI. One watt is about 3.412 BTU per hour. The area then follows in square feet or square metres respectively, and the overall coefficient must be in the matching set — mixing BTU-based U with a metric area is a frequent and large error.

Rearrange the duty equation: area equals duty divided by the product of the overall coefficient, the LMTD and the F factor. Every term carries uncertainty, but U is by far the least certain, so the area figure should be treated as a starting point for vendor selection rather than as a precise answer.

Not in the usual sense. When one stream is condensing at constant temperature, the flow arrangement no longer affects the driving force in the way it does for two sensible-heat streams, so F is effectively one. This is another reason steam-heated duties are simpler to calculate than liquid-to-liquid ones.

The logarithmic form divides by the log of one, which is zero, so the expression is undefined. The physical answer is simply that common value: if the driving force is the same at both ends it is the same throughout, and the log mean collapses to the arithmetic one. Calculators should handle this case explicitly rather than returning an error.

Only as an instantaneous value. The batch temperature rises continuously, so the driving force shrinks as the heat-up proceeds and no single LMTD describes the whole operation. Heat-up time comes from integrating over the batch temperature range, which is a different calculation using the same underlying equation.