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
lengthT140 °C90 °C?20 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 140 to 90 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 140 → 90 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
2.Easy
lengthT80 °C65 °C60 °C30 °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 80 to 65 °C and the cold fluid heats from 30 to 60 °C. Find the heat transfer rate Q̇.

A = 3 m²U = 1500 W/(m²·K)Th: 80 → 65 °CTc: 30 → 60 °C
Q̇ = kW
3.Medium
lengthT85 °C40 °C70 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 140 kW. The hot fluid cools from 85 to 40 °C and the cold fluid heats from 20 to 70 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 140 kWU = 200 W/(m²·K)Th: 85 → 40 °CTc: 20 → 70 °C
A = m²
4.Medium
lengthT155 °C70 °C115 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 120 kW. The hot fluid cools from 155 to 70 °C and the cold fluid heats from 10 to 115 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 120 kWU = 300 W/(m²·K)Th: 155 → 70 °CTc: 10 → 115 °C
A = m²
5.Hard
lengthT80 °C60 °C15.98 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 80 to 60 °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 kg/scp,h = 2.5 kJ/(kg·K)Th: 80 → 60 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT170 °C40 °C41.77 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 170 to 40 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 170 → 40 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 34.95 °C
  2. 2. Q̇ = 120.6 kW
  3. 3. A = 40.28 m²
  4. 4. A = 8.109 m²
  5. 5. A = 1.763 m²
  6. 6. A = 2.929 m²

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