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
lengthT135 °C55 °C50 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2 m² and an overall heat transfer coefficient of 200 W/(m²·K). The hot fluid cools from 135 to 55 °C and the cold fluid heats from 30 to 50 °C. Find the heat transfer rate Q̇.

A = 2 m²U = 200 W/(m²·K)Th: 135 → 55 °CTc: 30 → 50 °C
Q̇ = kW
2.Easy
lengthT125 °C75 °C105 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 125 to 75 °C while the cold fluid heats from 30 to 105 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 75 °CTc: 30 → 105 °C
ΔTlm = K
3.Medium
lengthT155 °C85 °C75 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 310 kW. The hot fluid cools from 155 to 85 °C and the cold fluid heats from 10 to 75 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 310 kWU = 1500 W/(m²·K)Th: 155 → 85 °CTc: 10 → 75 °C
A = m²
4.Medium
lengthT100 °C20 °C50 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 50 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 50 °CU = 3500 W/(m²·K)
A = m²
5.Hard
lengthT145 °C125 °C52.01 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 145 to 125 °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 = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 145 → 125 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT100 °C70 °C35.05 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 100 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 25 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 100 → 70 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 19.61 kW
  2. 2. ΔTlm = 30.83 K
  3. 3. A = 2.668 m²
  4. 4. A = 0.2807 m²
  5. 5. A = 0.9788 m²
  6. 6. A = 2.318 m²

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