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
lengthT100 °C55 °C50 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 12 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 100 to 55 °C and the cold fluid heats from 15 to 50 °C. Find the heat transfer rate Q̇.

A = 12 m²U = 800 W/(m²·K)Th: 100 → 55 °CTc: 15 → 50 °C
Q̇ = kW
2.Easy
lengthT130 °C65 °C75 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 5 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 130 to 65 °C and the cold fluid heats from 20 to 75 °C. Find the heat transfer rate Q̇.

A = 5 m²U = 300 W/(m²·K)Th: 130 → 65 °CTc: 20 → 75 °C
Q̇ = kW
3.Medium
lengthT135 °C110 °C20 °C35 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 270 kW. Its heat transfer area is 10 m². The hot fluid cools from 135 to 110 °C and the cold fluid heats from 20 to 35 °C. Find the overall heat transfer coefficient U.

Q̇ = 270 kWA = 10 m²Th: 135 → 110 °CTc: 20 → 35 °C
U = W/(m²·K)
4.Medium
lengthT130 °C60 °C15 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 460 kW. Its heat transfer area is 15 m². The hot fluid cools from 130 to 60 °C and the cold fluid heats from 15 to 50 °C. Find the overall heat transfer coefficient U.

Q̇ = 460 kWA = 15 m²Th: 130 → 60 °CTc: 15 → 50 °C
U = W/(m²·K)
5.Hard
lengthT155 °C95 °C135.6 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 95 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 95 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT175 °C140 °C46.38 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 175 to 140 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 175 → 140 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 430.2 kW
  2. 2. Q̇ = 74.75 kW
  3. 3. U = 288.5 W/(m²·K)
  4. 4. U = 713.3 W/(m²·K)
  5. 5. A = 3.926 m²
  6. 6. A = 2.957 m²

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