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
lengthT85 °C60 °C70 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 60 °C while the cold fluid heats from 15 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 60 °CTc: 15 → 70 °C
ΔTlm = K
2.Easy
lengthT120 °C80 °C70 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 80 °C while the cold fluid heats from 25 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 80 °CTc: 25 → 70 °C
ΔTlm = K
3.Medium
lengthT100 °C35 °C60 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 370 kW. The hot fluid cools from 100 to 35 °C and the cold fluid heats from 20 to 60 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 370 kWU = 300 W/(m²·K)Th: 100 → 35 °CTc: 20 → 60 °C
A = m²
4.Medium
lengthT95 °C55 °C10 °C20 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 280 kW. Its heat transfer area is 3 m². The hot fluid cools from 95 to 55 °C and the cold fluid heats from 10 to 20 °C. Find the overall heat transfer coefficient U.

Q̇ = 280 kWA = 3 m²Th: 95 → 55 °CTc: 10 → 20 °C
U = W/(m²·K)
5.Hard
lengthT110 °C55 °C48.42 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 110 to 55 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 110 → 55 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT165 °C70 °C35.91 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 165 to 70 °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 = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 165 → 70 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 27.31 K
  2. 2. ΔTlm = 52.46 K
  3. 3. A = 48.39 m²
  4. 4. U = 1656 W/(m²·K)
  5. 5. A = 18.98 m²
  6. 6. A = 2.392 m²

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