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Thermodynamics & Fluids · Heat Transfer

Heat exchangers

Reading27mLesson 3 of 3 in this module

Explain how shell-and-tube and plate heat exchangers work, why counterflow is preferred, and how the LMTD rates one.

Why it matters

Heat exchangers move heat from one fluid to another without letting them mix. They are everywhere: car radiators, home boilers, refrigerator condensers, power-plant condensers, the jackets on chemical reactors, pasteurisers in food and pharmaceutical plants, and the coolers on every large compressor. Knowing how they work, what the main types are, and how engineers rate them lets you read data sheets and follow design conversations, even before you design one yourself.

The basic idea

A hot fluid and a cold fluid flow on opposite sides of a solid wall (a tube or a plate). Heat passes from the hot fluid, by convection, to the wall; through the wall by conduction; and from the wall to the cold fluid by convection. Those three resistances in series combine into an overall heat transfer coefficient U, in W/(m²·K), just like the wall in the previous lesson. Fouling (scale, biofilm, corrosion products) adds more resistance over time, so designers include a fouling allowance and plan for cleaning.

Main types

  • Double-pipe: one tube inside another. Simple, good for small duties and teaching labs.
  • Shell-and-tube: a bundle of tubes inside a large shell. One fluid flows through the tubes, the other around them, guided back and forth by baffles. Rugged, handles high pressures and temperatures, easy to clean on the tube side. The workhorse of refineries, chemical plants and power stations.
  • Plate: stacked, corrugated metal plates with gaskets (or brazed or welded) forming thin alternating channels. Very high U and compact, easy to expand by adding plates, common in HVAC, food and dairy. Limited by gasket pressure and temperature ratings.
  • Finned-tube / air-cooled: fins increase the area on the air side, where h is low. Car radiators and air-conditioning coils.

Flow arrangement

  • Parallel flow: both fluids enter at the same end and flow the same way. The temperature difference is large at the inlet and shrinks along the exchanger; the cold outlet can never get hotter than the hot outlet.
  • Counterflow: the fluids flow in opposite directions. The temperature difference stays more even, and the cold fluid can leave hotter than the hot fluid's outlet. For the same duty, counterflow needs less area, so designers prefer it whenever practical.
  • Cross-flow: the fluids cross at right angles, typical of air-cooled coils. Shell-and-tube units with several passes behave between parallel and counterflow, handled with correction factors.

Rating an exchanger: energy balance and LMTD

Two equations do most of the work.

1. Energy balance. With no losses, the heat lost by the hot fluid equals the heat gained by the cold fluid:

Q = ṁ_h · c_p,h · (T_h,in − T_h,out) = ṁ_c · c_p,c · (T_c,out − T_c,in)

2. Rate equation. Because the temperature difference changes along the exchanger, it is averaged logarithmically:

Q = U · A · ΔT_lm        ΔT_lm = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2)

ΔT1 and ΔT2 are the temperature differences between the two fluids at each end.

Worked example. In a counterflow exchanger, hot water cools from 90 °C to 60 °C while cold water warms from 20 °C to 40 °C. U = 500 W/(m²·K) and A = 10 m².

Counterflow ends:  ΔT1 = 90 − 40 = 50 K     ΔT2 = 60 − 20 = 40 K
ΔT_lm = (50 − 40) / ln(50/40) = 10 / 0.2231 ≈ 44.8 K
Q = 500 × 10 × 44.8 ≈ 224 kW

When ΔT1 equals ΔT2 the formula gives 0/0; the LMTD then simply equals that common difference.

The effectiveness–NTU method (in brief)

When outlet temperatures are unknown, engineers use the effectiveness ε (actual heat transfer divided by the maximum possible) and the number of transfer units NTU = UA / C_min, with charts or formulas for each flow arrangement. You will meet it in a full heat transfer course; the idea is that bigger UA relative to the smaller heat capacity rate means outlets closer to the ideal.

Common mistakes

  • Using the arithmetic mean temperature difference instead of the LMTD. It overestimates when the end differences are very unequal.
  • Pairing the wrong ends. In counterflow, compare the hot inlet with the cold outlet, and the hot outlet with the cold inlet.
  • Ignoring fouling. A clean-condition U can drop a lot in service.
  • Forgetting the pressure side. Exchangers are pressure vessels; failures can release hot or hazardous fluids.

Codes and safety

Industrial shell-and-tube exchangers are pressure equipment, designed and fabricated to codes such as the ASME Boiler and Pressure Vessel Code and TEMA standards, and inspected under local rules. Their design and any repairs belong to qualified, often licensed, engineers and certified fabricators. Treat the numbers here as learning examples, not design values.

Recap

  • A heat exchanger transfers heat across a wall: convection, conduction, convection, combined in U.
  • Main types: double-pipe, shell-and-tube, plate, finned-tube.
  • Counterflow is the most effective arrangement.
  • Rate it with the energy balance and Q = U A ΔT_lm.

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