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
lengthT170 °C115 °C130 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 170 to 115 °C while the cold fluid heats from 20 to 130 °C. Find the log-mean temperature difference ΔTlm.

Th: 170 → 115 °CTc: 20 → 130 °C
ΔTlm = K
2.Easy
lengthT140 °C50 °C?15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 140 to 50 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 140 → 50 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
3.Medium
lengthT150 °C90 °C30 °C75 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 450 kW. The hot fluid cools from 150 to 90 °C and the cold fluid heats from 30 to 75 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 450 kWU = 200 W/(m²·K)Th: 150 → 90 °CTc: 30 → 75 °C
A = m²
4.Medium
lengthT180 °C95 °C45 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 160 kW. Its heat transfer area is 10 m². The hot fluid cools from 180 to 95 °C and the cold fluid heats from 25 to 45 °C. Find the overall heat transfer coefficient U.

Q̇ = 160 kWA = 10 m²Th: 180 → 95 °CTc: 25 → 45 °C
U = W/(m²·K)
5.Hard
lengthT150 °C80 °C107 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 150 to 80 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 150 → 80 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT155 °C65 °C41.3 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 65 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 65 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 63.58 K
  2. 2. Tc,out = 39.76 °C
  3. 3. A = 44.56 m²
  4. 4. U = 161.7 W/(m²·K)
  5. 5. A = 6.94 m²
  6. 6. A = 0.9432 m²

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