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 °C85 °C85 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 85 °C while the cold fluid heats from 30 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 85 °CTc: 30 → 85 °C
ΔTlm = K
2.Easy
lengthT145 °C75 °C55 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 8 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 145 to 75 °C and the cold fluid heats from 30 to 55 °C. Find the heat transfer rate Q̇.

A = 8 m²U = 300 W/(m²·K)Th: 145 → 75 °CTc: 30 → 55 °C
Q̇ = kW
3.Medium
lengthT145 °C50 °C30 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 100 kW. The hot fluid cools from 145 to 50 °C and the cold fluid heats from 20 to 30 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 100 kWU = 300 W/(m²·K)Th: 145 → 50 °CTc: 20 → 30 °C
A = m²
4.Medium
lengthT150 °C75 °C110 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 420 kW. The hot fluid cools from 150 to 75 °C and the cold fluid heats from 20 to 110 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 420 kWU = 1500 W/(m²·K)Th: 150 → 75 °CTc: 20 → 110 °C
A = m²
5.Hard
lengthT115 °C45 °C38.44 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 115 to 45 °C in a counter-flow exchanger. It heats 3 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 = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 115 → 45 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT155 °C135 °C72.85 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 155 to 135 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 155 → 135 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 41.24 K
  2. 2. Q̇ = 155.8 kW
  3. 3. A = 5.27 m²
  4. 4. A = 5.944 m²
  5. 5. A = 29.58 m²
  6. 6. A = 1.048 m²

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