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
lengthT105 °C70 °C40 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 105 to 70 °C while the cold fluid heats from 15 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 70 °CTc: 15 → 40 °C
ΔTlm = K
2.Easy
lengthT135 °C120 °C110 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 120 °C while the cold fluid heats from 20 to 110 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 120 °CTc: 20 → 110 °C
ΔTlm = K
3.Medium
lengthT175 °C130 °C20 °C115 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 80 kW. Its heat transfer area is 2.5 m². The hot fluid cools from 175 to 130 °C and the cold fluid heats from 20 to 115 °C. Find the overall heat transfer coefficient U.

Q̇ = 80 kWA = 2.5 m²Th: 175 → 130 °CTc: 20 → 115 °C
U = W/(m²·K)
4.Medium
lengthT90 °C50 °C70 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 460 kW. The hot fluid cools from 90 to 50 °C and the cold fluid heats from 15 to 70 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 460 kWU = 1000 W/(m²·K)Th: 90 → 50 °CTc: 15 → 70 °C
A = m²
5.Hard
lengthT110 °C55 °C47.89 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 110 to 55 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 110 → 55 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT150 °C50 °C75.02 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 150 to 50 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 150 → 50 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 59.86 K
  2. 2. ΔTlm = 54.1 K
  3. 3. U = 533.8 W/(m²·K)
  4. 4. A = 17.16 m²
  5. 5. A = 6.842 m²
  6. 6. A = 46.84 m²

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