Heat exchangers (LMTD) worksheet with answers

Free printable Heat exchangers (LMTD) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
lengthT80 °C60 °C20 °C55 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 80 to 60 °C while the cold fluid heats from 20 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 80 → 60 °CTc: 20 → 55 °C
ΔTlm = K
2.Easy
lengthT135 °C110 °C20 °C100 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 135 to 110 °C while the cold fluid heats from 20 to 100 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 110 °CTc: 20 → 100 °C
ΔTlm = K
3.Medium
lengthT80 °C35 °C50 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 230 kW. Its heat transfer area is 3 m². The hot fluid cools from 80 to 35 °C and the cold fluid heats from 10 to 50 °C. Find the overall heat transfer coefficient U.

Q̇ = 230 kWA = 3 m²Th: 80 → 35 °CTc: 10 → 50 °C
U = W/(m²·K)
4.Medium
lengthT170 °C155 °C20 °C130 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 410 kW. The hot fluid cools from 170 to 155 °C and the cold fluid heats from 20 to 130 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 410 kWU = 1500 W/(m²·K)Th: 170 → 155 °CTc: 20 → 130 °C
A = m²
5.Hard
lengthT140 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 140 °C on the outside of the tubes of a condenser with a heat transfer area of 3 m² and U = 3000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 3 m²U = 3000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT150 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 150 °C and the cold stream at 25 °C. The exchanger has A = 1 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 150 °CTc,in = 25 °CA = 1 m²U = 800 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 22.13 K
  2. 2. ΔTlm = 42.99 K
  3. 3. U = 2796 W/(m²·K)
  4. 4. A = 3.918 m²
  5. 5. Tc,out = 83.89 °C
  6. 6. Th,out = 94.44 °C

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