Heat Exchanger

Calc

Heat Exchanger Design Theory

Introduction

Heat exchangers are devices that transfer thermal energy between two or more fluids at different temperatures. They are widely used in chemical processing, power generation, HVAC systems, and many other industrial applications.

Two primary methods are used for heat exchanger design and analysis: the Log Mean Temperature Difference (LMTD) method and the Effectiveness-NTU (ε-NTU) method.

LMTD Method

The LMTD method is based on the fundamental heat transfer equation:

Q = U × A × F × ΔTlm

Where:

  • Q = Heat transfer rate (kW)
  • U = Overall heat transfer coefficient (W/m²·K)
  • A = Heat transfer area (m²)
  • F = LMTD correction factor (dimensionless)
  • ΔTlm = Log mean temperature difference (°C)

Calculating LMTD

For a counterflow heat exchanger:

ΔTlm = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂)

Where:

  • ΔT₁ = Th,in - Tc,out (hot inlet - cold outlet)
  • ΔT₂ = Th,out - Tc,in (hot outlet - cold inlet)

LMTD Correction Factor (F)

For shell-and-tube and crossflow heat exchangers, a correction factor F is applied to account for the deviation from pure counterflow operation:

  • Counterflow: F = 1.0 (pure counterflow)
  • Parallel flow: F = 1.0 (uses different LMTD calculation)
  • Shell-tube (1-2): F = 0.7 - 1.0 (depends on P and R)
  • Crossflow: F = 0.75 - 1.0

The correction factor depends on two dimensionless parameters P and R, which characterize the temperature effectiveness and capacity rate ratio.

Effectiveness-NTU Method

The ε-NTU method is particularly useful when outlet temperatures are unknown (rating problems).

Key Parameters

Heat Capacity Rates:

Ch = ṁh × cp,h

Cc = ṁc × cp,c

Cmin = min(Ch, Cc)

Cr = Cmin / Cmax

Effectiveness:

ε = Q / Qmax = Q / (Cmin × (Th,in - Tc,in))

Number of Transfer Units:

NTU = UA / Cmin

ε-NTU Relations

For a counterflow heat exchanger:

If Cr < 1:

ε = (1 - exp(-NTU × (1 - Cr))) / (1 - Cr × exp(-NTU × (1 - Cr)))

If Cr = 1:

ε = NTU / (1 + NTU)

Design vs Rating Mode

Design Mode

Given: Inlet/outlet temperatures, flow rates

Find: Required heat transfer area (A), UA value

Rating Mode

Given: Inlet temperatures, flow rates, UA or area

Find: Outlet temperatures, actual heat duty

Flow Arrangements

Counterflow

Fluids flow in opposite directions. Most thermally efficient arrangement. Can achieve closest approach temperatures.

Parallel Flow

Fluids flow in the same direction. Limited by the average of inlet temperatures. Lower effectiveness than counterflow.

Shell-Tube (1-2)

One shell pass, two tube passes. Common industrial configuration. Requires LMTD correction factor.

Crossflow

Fluids flow perpendicular to each other. Common in air-cooled exchangers. Intermediate effectiveness.

References

  • • Incropera, F.P., & DeWitt, D.P. "Fundamentals of Heat and Mass Transfer"
  • • Kakac, S., & Liu, H. "Heat Exchangers: Selection, Rating, and Thermal Design"
  • • TEMA Standards (Tubular Exchanger Manufacturers Association)