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
lengthT115 °C35 °C30 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 35 °C while the cold fluid heats from 15 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 35 °CTc: 15 → 30 °C
ΔTlm = K
2.Easy
lengthT110 °C90 °C30 °C85 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 110 to 90 °C while the cold fluid heats from 30 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 90 °CTc: 30 → 85 °C
ΔTlm = K
3.Medium
lengthT175 °C115 °C25 °C100 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 270 kW. Its heat transfer area is 6 m². The hot fluid cools from 175 to 115 °C and the cold fluid heats from 25 to 100 °C. Find the overall heat transfer coefficient U.

Q̇ = 270 kWA = 6 m²Th: 175 → 115 °CTc: 25 → 100 °C
U = W/(m²·K)
4.Medium
lengthT170 °C130 °C30 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 340 kW. Its heat transfer area is 1 m². The hot fluid cools from 170 to 130 °C and the cold fluid heats from 20 to 30 °C. Find the overall heat transfer coefficient U.

Q̇ = 340 kWA = 1 m²Th: 170 → 130 °CTc: 20 → 30 °C
U = W/(m²·K)
5.Hard
lengthT125 °C50 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 125 to 50 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 50 mm, and U = 150 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 125 → 50 °Cṁc = 0.5 kg/sTc,in = 15 °CD = 50 mmU = 150 W/(m²·K)
L = m
6.Hard
lengthT160 °C65 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.2 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 160 to 65 °C. Water (0.3 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 25 mm, and U = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.2 kg/scp,h = 2.5 kJ/(kg·K)Th: 160 → 65 °Cṁc = 0.3 kg/sTc,in = 15 °CD = 25 mmU = 250 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 44.92 K
  2. 2. ΔTlm = 27.05 K
  3. 3. U = 767.5 W/(m²·K)
  4. 4. U = 2733 W/(m²·K)
  5. 5. L = 295 m
  6. 6. L = 32.27 m

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