Heat Exchanger LMTD Helper

Calculate the Log Mean Temperature Difference (LMTD) for parallel and counterflow heat exchangers. Compute end temperature differences, apply correction factors, and solve Q = U × A × ΔT relationships.

Heat Exchanger Configuration

Units

Decimal Places

1Case 1(Counterflow)

Case Label (optional)

Flow Arrangement

Stream Temperatures

Hot Fluid

T_h,in (inlet)

T_h,out (outlet)

Cold Fluid

T_c,in (inlet)

T_c,out (outlet)

ΔT Override (optional)

ΔT₁

ΔT₂

Performance Parameters

U (W/m²·K)

A (m²)

Q (W)

Correction Factor F (optional)

Notes (optional)

Get a quick LMTD for your heat exchanger

Choose parallel or counterflow, enter inlet and outlet temperatures for both fluids, and we'll compute ΔT₁, ΔT₂, and the log mean temperature difference. Add U, A, or Q to see how they relate.

Start with a simple example, like a counterflow exchanger with known inlet and outlet temperatures on both sides.

Understanding Heat Exchanger LMTD

What Is LMTD in a Heat Exchanger?

In a heat exchanger, the temperature difference between the hot and cold fluids changes along the length of the device. At one end, the difference might be large; at the other end, it might be smaller. The Log Mean Temperature Difference (LMTD) is a single "average" temperature difference that, when used in the equation Q = U × A × ΔT_lm, gives the correct heat transfer rate for steady-state conditions.

LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁ / ΔT₂)

where ΔT₁ and ΔT₂ are the temperature differences at each end of the heat exchanger.

Parallel vs Counterflow LMTD

The definition of ΔT₁ and ΔT₂ depends on the flow arrangement:

Parallel Flow

• Both fluids enter at the same end
• ΔT₁ = T_h,in - T_c,in
• ΔT₂ = T_h,out - T_c,out
• Temperature differences always converge

Counterflow

• Fluids enter at opposite ends
• ΔT₁ = T_h,in - T_c,out
• ΔT₂ = T_h,out - T_c,in
• More efficient; often yields higher LMTD

Counterflow heat exchangers generally produce a higher LMTD for the same terminal temperatures, making them more thermally efficient. They can also achieve closer approach temperatures (T_c,out> T_h,out is possible in counterflow).

Using LMTD with U, A, and Q

The key design equation for heat exchangers is:

Q = U × A × ΔT_lm,eff

Q = Heat transfer rate (W)
U = Overall heat transfer coefficient (W/m²·K)
A = Heat transfer area (m²)
ΔT_lm,eff = Effective LMTD = F × LMTD

Given any three of these quantities, you can solve for the fourth. This tool helps you explore these relationships quickly.

Correction Factor F (Simplified View)

Real heat exchangers often have flow patterns that are not purely parallel or counterflow. Shell-and-tube exchangers with multiple passes, cross-flow designs, and other configurations have mixed flow that reduces the effective temperature difference.

The correction factor F adjusts the ideal LMTD:

ΔT_lm,eff = F × LMTD

This tool does not compute F from detailed geometry. If you know F from charts or correlations (e.g., TEMA standards), enter it; otherwise, results assume F = 1 (pure parallel or counterflow).

Limitations & Assumptions

Steady-state conditions: No time-dependent behavior or startup transients.
Constant properties: U is assumed constant along the exchanger length.
No internal heat generation: Heat transfer is driven only by the temperature difference between streams.
No phase change modeling: Condensation or boiling is handled implicitly through user-supplied temperatures and U values.
No pressure drop: This tool focuses on thermal analysis only.
Educational purposes: For real design, use professional tools and consult qualified engineers.

Heat Exchanger LMTD FAQ

Common questions about log mean temperature difference and heat exchanger calculations.

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