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
lengthT140 °C60 °C65 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 140 to 60 °C while the cold fluid heats from 30 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 60 °CTc: 30 → 65 °C
ΔTlm = K
2.Easy
lengthT135 °C100 °C50 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 100 °C while the cold fluid heats from 30 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 100 °CTc: 30 → 50 °C
ΔTlm = K
3.Medium
lengthT155 °C55 °C100 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 680 kW. The hot fluid cools from 155 to 55 °C and the cold fluid heats from 20 to 100 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 680 kWF = 0.95U = 300 W/(m²·K)Th: 155 → 55 °CTc: 20 → 100 °C
A = m²
4.Medium
lengthT125 °C70 °C20 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 500 kW. Its heat transfer area is 6 m². The hot fluid cools from 125 to 70 °C and the cold fluid heats from 20 to 40 °C. Find the overall heat transfer coefficient U.

Q̇ = 500 kWA = 6 m²Th: 125 → 70 °CTc: 20 → 40 °C
U = W/(m²·K)
5.Hard
lengthT100 °C70 °C36 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 100 to 70 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 100 → 70 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT140 °C90 °C35.12 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 140 to 90 °C in a counter-flow exchanger. It heats 0.5 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: 140 → 90 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 49.11 K
  2. 2. ΔTlm = 77.26 K
  3. 3. A = 53.92 m²
  4. 4. U = 1392 W/(m²·K)
  5. 5. A = 8.528 m²
  6. 6. A = 1.143 m²

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