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
lengthT170 °C115 °C135 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 170 to 115 °C while the cold fluid heats from 30 to 135 °C. Find the log-mean temperature difference ΔTlm.

Th: 170 → 115 °CTc: 30 → 135 °C
ΔTlm = K
2.Easy

In a heat exchanger 3 kg/s of glycol mix (cp = 3.6 kJ/(kg·K)) is heated from 10 to 40 °C. Find the heat transfer rate Q̇.

ṁ = 3 kg/scp = 3.6 kJ/(kg·K)T: 10 → 40 °C
Q̇ = kW
3.Medium
lengthT105 °C55 °C20 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 450 kW. Its heat transfer area is 4 m². The hot fluid cools from 105 to 55 °C and the cold fluid heats from 20 to 50 °C. Find the overall heat transfer coefficient U.

Q̇ = 450 kWA = 4 m²Th: 105 → 55 °CTc: 20 → 50 °C
U = W/(m²·K)
4.Medium
lengthT140 °C20 °C60 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 60 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 60 °CU = 1000 W/(m²·K)
A = m²
5.Hard
lengthT120 °C85 °C20.47 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 85 °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 = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 85 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT95 °C60 °C36.98 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 95 to 60 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 95 → 60 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 56.35 K
  2. 2. Q̇ = 324 kW
  3. 3. U = 3984 W/(m²·K)
  4. 4. A = 2.542 m²
  5. 5. A = 0.6729 m²
  6. 6. A = 6.866 m²

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