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
lengthT90 °C45 °C50 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 45 °C while the cold fluid heats from 10 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 45 °CTc: 10 → 50 °C
ΔTlm = K
2.Easy
lengthT105 °C70 °C40 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 8 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 105 to 70 °C and the cold fluid heats from 25 to 40 °C. Find the heat transfer rate Q̇.

A = 8 m²U = 300 W/(m²·K)Th: 105 → 70 °CTc: 25 → 40 °C
Q̇ = kW
3.Medium
lengthT105 °C45 °C30 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 340 kW. The hot fluid cools from 105 to 45 °C and the cold fluid heats from 20 to 30 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 340 kWU = 200 W/(m²·K)Th: 105 → 45 °CTc: 20 → 30 °C
A = m²
4.Medium
lengthT100 °C85 °C30 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 330 kW. The hot fluid cools from 100 to 85 °C and the cold fluid heats from 30 to 50 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 330 kWU = 800 W/(m²·K)Th: 100 → 85 °CTc: 30 → 50 °C
A = m²
5.Hard
lengthT120 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 120 °C on the outside of the tubes of a condenser with a heat transfer area of 3 m² and U = 1000 W/(m²·K). Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 120 °CA = 3 m²U = 1000 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT110 °C30 °C45.89 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 110 to 30 °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 = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 110 → 30 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 37.44 K
  2. 2. Q̇ = 130.5 kW
  3. 3. A = 37.35 m²
  4. 4. A = 8.169 m²
  5. 5. Tc,out = 96.2 °C
  6. 6. A = 15.84 m²

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