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 °C65 °C40 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 65 °C while the cold fluid heats from 25 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 65 °CTc: 25 → 40 °C
ΔTlm = K
2.Easy
lengthT135 °C85 °C25 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 85 °C while the cold fluid heats from 10 to 25 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 85 °CTc: 10 → 25 °C
ΔTlm = K
3.Medium
lengthT95 °C60 °C25 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 130 kW. The hot fluid cools from 95 to 60 °C and the cold fluid heats from 25 to 40 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 130 kWU = 1000 W/(m²·K)Th: 95 → 60 °CTc: 25 → 40 °C
A = m²
4.Medium
lengthT110 °C35 °C60 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 200 kW. The hot fluid cools from 110 to 35 °C and the cold fluid heats from 10 to 60 °C. The LMTD correction factor for this arrangement is F = 0.8, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 200 kWF = 0.8U = 500 W/(m²·K)Th: 110 → 35 °CTc: 10 → 60 °C
A = m²
5.Hard
lengthT155 °C120 °C14.4 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 120 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 120 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT135 °C105 °C65.89 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 135 to 105 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 135 → 105 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 42.45 K
  2. 2. ΔTlm = 91.39 K
  3. 3. A = 3.257 m²
  4. 4. A = 13.86 m²
  5. 5. A = 0.9825 m²
  6. 6. A = 5.207 m²

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