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 °C125 °C75 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 145 to 125 °C while the cold fluid heats from 30 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 125 °CTc: 30 → 75 °C
ΔTlm = K
2.Easy

In a heat exchanger 1 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is cooled from 90 to 45 °C. Find the heat transfer rate Q̇.

ṁ = 1 kg/scp = 2.1 kJ/(kg·K)T: 90 → 45 °C
Q̇ = kW
3.Medium
lengthT170 °C140 °C25 °C125 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 170 kW. The hot fluid cools from 170 to 140 °C and the cold fluid heats from 25 to 125 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 170 kWU = 800 W/(m²·K)Th: 170 → 140 °CTc: 25 → 125 °C
A = m²
4.Medium
lengthT120 °C100 °C25 °C55 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 380 kW. The hot fluid cools from 120 to 100 °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 = 380 kWU = 200 W/(m²·K)Th: 120 → 100 °CTc: 25 → 55 °C
A = m²
5.Hard
lengthT140 °C50 °C83.83 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 140 to 50 °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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 140 → 50 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT80 °C55 °C29.97 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 80 to 55 °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 = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 80 → 55 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 81.86 K
  2. 2. Q̇ = 94.5 kW
  3. 3. A = 3.708 m²
  4. 4. A = 28.39 m²
  5. 5. A = 4.015 m²
  6. 6. A = 0.9904 m²

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