Heat Exchanger LMTD Duty Area Calculator

The Heat Exchanger LMTD, Duty and Area Calculator works out the log mean temperature difference from four terminal temperatures, and then either rates the heat duty from an overall coefficient and an area, or solves the area required to reach a duty you specify.

It runs in three modes. LMTD only reports the driving force and the two terminal approaches and nothing else. Heat duty from U and area returns the duty and the UA product. Required area from heat duty and U returns the area and the UA that duty implies. Whichever inputs a mode does not need are hidden and take no part in the result.

It offers ideal counterflow and ideal parallel flow. Crossflow and multipass shell-and-tube arrangements are deliberately excluded, and that matters more than it sounds: there is no F correction factor anywhere in this calculator. If your exchanger is anything other than pure counterflow or pure parallel flow, the duty it returns is too high and the area too small, and nothing on the page will say so.

It accepts SI metric or US customary entry. Changing the selector relabels the fields and switches the internal unit path. It does not convert values you have already typed.

It is a thermal rating screen. There are no flow rates in it, so it never checks that the four temperatures you entered are consistent with each other or with the duty it reports, and it selects no exchanger.

Purpose and model boundary

This model calculates log mean temperature difference for ideal counterflow or parallel-flow terminal temperatures. It can rate heat duty from user-entered U and area or solve the area required for an entered duty. It is a thermal screen, not an exchanger selection, correction-factor, pressure-drop, mechanical-design, or code-compliance tool.

Inputs and units

The unit-system selector switches the displayed temperature, overall-coefficient, duty, and area units while the workbook converts through its common internal basis. The user selects flow arrangement and calculation mode, enters hot- and cold-stream inlet/outlet temperatures, and supplies an overall heat-transfer coefficient. Rating mode uses entered area; sizing mode uses target heat duty.

Governing relationships

For counterflow:

ΔT_1 = T_hot,in - T_cold,out

ΔT_2 = T_hot,out - T_cold,in

For parallel flow:

ΔT_1 = T_hot,in - T_cold,in

ΔT_2 = T_hot,out - T_cold,out

For positive terminal approaches:

LMTD = (ΔT_1 - ΔT_2) / ln(ΔT_1 / ΔT_2)

When the approaches are equal, the workbook uses the continuous limit LMTD = ΔT_1 = ΔT_2 rather than dividing zero by zero. The exchanger conductance and the two solve modes are:

UA = U × A

Q = U × A × LMTD

A_required = Q_target / (U × LMTD)

The chart connects the entered terminal temperatures to illustrate the selected stream arrangement; it is not an internally solved temperature distribution.

Calculation sequence

1. Validate unit, mode, and arrangement selections plus the active temperatures, U, area, or target duty.
2. Confirm the temperature ordering and both selected terminal approaches are positive.
3. Calculate ΔT_1, ΔT_2, and the equal-approach-safe LMTD.
4. Calculate UA and either heat duty or required area according to the selected mode.
5. Build the terminal-profile series and evaluate status in the order below.

Outputs and interpretation

The visible headline changes with calculation mode: rating exposes heat duty, sizing exposes required area, and both expose LMTD. Supporting values include both terminal differences, UA, and a terminal-profile assessment. A valid LMTD confirms only the arithmetic relationship among the entered terminal temperatures; it does not confirm that a real exchanger can achieve them.

Validation and status logic

This is the exact precedence of the workbook Model_Status formula. Invalid states return protected zero numeric outputs; they are not valid zero-duty or zero-area findings.

Assumptions and limitations

• The terminal temperatures describe one steady operating point and the selected pure parallel-flow or counterflow arrangement.
• Properties and U are treated as sufficiently constant. Entered U must already include the intended film, wall, fouling, geometry, and area-basis effects.
• Crossflow, multipass, and other arrangements requiring an LMTD correction factor are outside scope; no correction-factor chart is embedded.
• The workbook has no fluid properties, phase-equilibrium data, fouling-factor table, exchanger catalog, or manufacturer performance data.
• Pressure drop, vibration, thermal stress, materials compatibility, corrosion, relief, nozzle loads, fabrication, and inspection are outside scope.
• Isothermal terminal data can represent an assumed phase-change stream, but latent duty and quality are not verified.

Restrictions and non-computing states

Both terminal approaches must remain positive, the hot stream must not heat across the exchanger, and the cold stream must not cool. U must be positive. Rating mode requires positive area; sizing mode allows zero target duty but reports the explicit check above. Inputs outside the published limits or undeclared dropdown values are rejected before calculation.

Errors and warnings

NOT VALID blocks interpretation of the numeric outputs. CHECK leaves arithmetic available for an intentional zero-duty or isothermal case but flags the assumption requiring review. A connection or calculation-service failure is not an exchanger assessment.

The relationships, mode visibility, status precedence, and named-output formulas were verified against the delivered workbook, its published input rules, tests, and reviewer packet. The workbook identifies these technical sources:

• DOE-HDBK-1012/2-92, Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2 — Log mean temperature difference and the Q = U A LMTD relationship.
• NIST Guide to the SI, Appendix B — Exact length and area conversions.
• NIST Guide to the SI, Chapter 8 — Temperature-interval conversions.