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
lengthT105 °C75 °C?20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 105 to 75 °C in a counter-flow exchanger. It heats 0.8 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 = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 105 → 75 °Cṁc = 0.8 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
2.Easy
lengthT135 °C35 °C30 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2.5 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 135 to 35 °C and the cold fluid heats from 15 to 30 °C. Find the heat transfer rate Q̇.

A = 2.5 m²U = 500 W/(m²·K)Th: 135 → 35 °CTc: 15 → 30 °C
Q̇ = kW
3.Medium
lengthT105 °C85 °C80 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 310 kW. Its heat transfer area is 3 m². The hot fluid cools from 105 to 85 °C and the cold fluid heats from 10 to 80 °C. Find the overall heat transfer coefficient U.

Q̇ = 310 kWA = 3 m²Th: 105 → 85 °CTc: 10 → 80 °C
U = W/(m²·K)
4.Medium
lengthT125 °C50 °C50 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 300 kW. Its heat transfer area is 3 m². The hot fluid cools from 125 to 50 °C and the cold fluid heats from 30 to 50 °C. Find the overall heat transfer coefficient U.

Q̇ = 300 kWA = 3 m²Th: 125 → 50 °CTc: 30 → 50 °C
U = W/(m²·K)
5.Hard
lengthT115 °C40 °C59.86 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 115 to 40 °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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 115 → 40 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT85 °C55 °C23.46 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 85 to 55 °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 = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 85 → 55 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 29.42 °C
  2. 2. Q̇ = 64.07 kW
  3. 3. U = 2270 W/(m²·K)
  4. 4. U = 2403 W/(m²·K)
  5. 5. A = 3.075 m²
  6. 6. A = 2.129 m²

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