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
lengthT175 °C85 °C60 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 85 °C while the cold fluid heats from 25 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 85 °CTc: 25 → 60 °C
ΔTlm = K
2.Easy
lengthT95 °C70 °C50 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 70 °C while the cold fluid heats from 20 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 70 °CTc: 20 → 50 °C
ΔTlm = K
3.Medium
lengthT135 °C95 °C40 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 180 kW. Its heat transfer area is 20 m². The hot fluid cools from 135 to 95 °C and the cold fluid heats from 30 to 40 °C. Find the overall heat transfer coefficient U.

Q̇ = 180 kWA = 20 m²Th: 135 → 95 °CTc: 30 → 40 °C
U = W/(m²·K)
4.Medium
lengthT140 °C120 °C25 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 410 kW. The hot fluid cools from 140 to 120 °C and the cold fluid heats from 25 to 60 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 410 kWU = 800 W/(m²·K)Th: 140 → 120 °CTc: 25 → 60 °C
A = m²
5.Hard
lengthT160 °C115 °C20 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.8 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 160 to 115 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °C. The inner tube has a diameter of 50 mm, and U = 200 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.8 kg/scp,h = 2.5 kJ/(kg·K)Th: 160 → 115 °Cṁc = 1.5 kg/sTc,in = 20 °CD = 50 mmU = 200 W/(m²·K)
L = m
6.Hard
lengthT110 °C80 °C20 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 110 to 80 °C. Water (0.8 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °C. The inner tube has a diameter of 40 mm, and U = 300 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 110 → 80 °Cṁc = 0.8 kg/sTc,in = 20 °CD = 40 mmU = 300 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 84.54 K
  2. 2. ΔTlm = 47.46 K
  3. 3. U = 113.8 W/(m²·K)
  4. 4. A = 6.062 m²
  5. 5. L = 26.62 m
  6. 6. L = 14.78 m

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