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
lengthT150 °C65 °C105 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 150 to 65 °C while the cold fluid heats from 10 to 105 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 65 °CTc: 10 → 105 °C
ΔTlm = K
2.Easy
lengthT85 °C50 °C70 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 50 °C while the cold fluid heats from 30 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 50 °CTc: 30 → 70 °C
ΔTlm = K
3.Medium
lengthT155 °C40 °C40 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 390 kW. The hot fluid cools from 155 to 40 °C and the cold fluid heats from 15 to 40 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWU = 500 W/(m²·K)Th: 155 → 40 °CTc: 15 → 40 °C
A = m²
4.Medium
lengthT180 °C135 °C10 °C70 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 390 kW. Its heat transfer area is 12 m². The hot fluid cools from 180 to 135 °C and the cold fluid heats from 10 to 70 °C. Find the overall heat transfer coefficient U.

Q̇ = 390 kWA = 12 m²Th: 180 → 135 °CTc: 10 → 70 °C
U = W/(m²·K)
5.Hard
lengthT120 °C55 °C62.66 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 120 to 55 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 120 → 55 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT130 °C40 °C17.54 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 130 to 40 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °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: 130 → 40 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 49.83 K
  2. 2. ΔTlm = 17.38 K
  3. 3. A = 13.23 m²
  4. 4. U = 297.6 W/(m²·K)
  5. 5. A = 14.01 m²
  6. 6. A = 3.029 m²

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