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
lengthT180 °C60 °C150 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 6 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 180 to 60 °C and the cold fluid heats from 20 to 150 °C. Find the heat transfer rate Q̇.

A = 6 m²U = 500 W/(m²·K)Th: 180 → 60 °CTc: 20 → 150 °C
Q̇ = kW
2.Easy
lengthT90 °C40 °C30 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 3 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 90 to 40 °C and the cold fluid heats from 20 to 30 °C. Find the heat transfer rate Q̇.

A = 3 m²U = 1500 W/(m²·K)Th: 90 → 40 °CTc: 20 → 30 °C
Q̇ = kW
3.Medium
lengthT120 °C90 °C105 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 50 kW. The hot fluid cools from 120 to 90 °C and the cold fluid heats from 25 to 105 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 50 kWU = 200 W/(m²·K)Th: 120 → 90 °CTc: 25 → 105 °C
A = m²
4.Medium
lengthT145 °C125 °C40 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 320 kW. The hot fluid cools from 145 to 125 °C and the cold fluid heats from 10 to 40 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 320 kWU = 1500 W/(m²·K)Th: 145 → 125 °CTc: 10 → 40 °C
A = m²
5.Hard
lengthT165 °C115 °C24.98 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 165 to 115 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 165 → 115 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT150 °C95 °C58.86 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 150 to 95 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 150 → 95 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 104.3 kW
  2. 2. Q̇ = 163.8 kW
  3. 3. A = 7.332 m²
  4. 4. A = 1.941 m²
  5. 5. A = 2.693 m²
  6. 6. A = 3.218 m²

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