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
lengthT120 °C105 °C65 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 105 °C while the cold fluid heats from 15 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 105 °CTc: 15 → 65 °C
ΔTlm = K
2.Easy
lengthT130 °C100 °C120 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 100 °C while the cold fluid heats from 25 to 120 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 100 °CTc: 25 → 120 °C
ΔTlm = K
3.Medium
lengthT155 °C55 °C40 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 80 kW. The hot fluid cools from 155 to 55 °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 = 80 kWU = 300 W/(m²·K)Th: 155 → 55 °CTc: 30 → 40 °C
A = m²
4.Medium
lengthT170 °C155 °C15 °C75 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 140 kW. The hot fluid cools from 170 to 155 °C and the cold fluid heats from 15 to 75 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 140 kWU = 1000 W/(m²·K)Th: 170 → 155 °CTc: 15 → 75 °C
A = m²
5.Hard
lengthT125 °C100 °C29.17 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 125 to 100 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 125 → 100 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT85 °C50 °C30.93 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 85 to 50 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 85 → 50 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 71.07 K
  2. 2. ΔTlm = 32.26 K
  3. 3. A = 4.522 m²
  4. 4. A = 1.235 m²
  5. 5. A = 1.312 m²
  6. 6. A = 1.874 m²

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