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
lengthT145 °C100 °C65 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 145 to 100 °C while the cold fluid heats from 30 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 100 °CTc: 30 → 65 °C
ΔTlm = K
2.Easy
lengthT155 °C95 °C145 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 95 °C while the cold fluid heats from 15 to 145 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 95 °CTc: 15 → 145 °C
ΔTlm = K
3.Medium
lengthT90 °C55 °C55 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 480 kW. The hot fluid cools from 90 to 55 °C and the cold fluid heats from 25 to 55 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 480 kWU = 200 W/(m²·K)Th: 90 → 55 °CTc: 25 → 55 °C
A = m²
4.Medium
lengthT95 °C60 °C85 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 180 kW. The hot fluid cools from 95 to 60 °C and the cold fluid heats from 20 to 85 °C. The LMTD correction factor for this arrangement is F = 0.8, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 180 kWF = 0.8U = 1000 W/(m²·K)Th: 95 → 60 °CTc: 20 → 85 °C
A = m²
5.Hard
lengthT145 °C100 °C31.73 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 145 to 100 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 145 → 100 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT90 °C70 °C34.67 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 90 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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 90 → 70 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 74.89 K
  2. 2. ΔTlm = 33.66 K
  3. 3. A = 73.99 m²
  4. 4. A = 10.4 m²
  5. 5. A = 0.606 m²
  6. 6. A = 2.186 m²

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