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
lengthT155 °C120 °C75 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 120 °C while the cold fluid heats from 10 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 120 °CTc: 10 → 75 °C
ΔTlm = K
2.Easy
lengthT145 °C95 °C25 °C55 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 145 to 95 °C while the cold fluid heats from 25 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 95 °CTc: 25 → 55 °C
ΔTlm = K
3.Medium
lengthT145 °C130 °C100 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 340 kW. The hot fluid cools from 145 to 130 °C and the cold fluid heats from 25 to 100 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 340 kWU = 300 W/(m²·K)Th: 145 → 130 °CTc: 25 → 100 °C
A = m²
4.Medium
lengthT90 °C50 °C30 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 390 kW. The hot fluid cools from 90 to 50 °C and the cold fluid heats from 30 to 40 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWU = 300 W/(m²·K)Th: 90 → 50 °CTc: 30 → 40 °C
A = m²
5.Hard
lengthT160 °C65 °C49.85 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 160 to 65 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 160 → 65 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT175 °C95 °C85.29 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 175 to 95 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 175 → 95 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 94.21 K
  2. 2. ΔTlm = 72.82 K
  3. 3. A = 16 m²
  4. 4. A = 46.59 m²
  5. 5. A = 1.913 m²
  6. 6. A = 3.965 m²

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