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 °C115 °C25 °C50 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 140 to 115 °C while the cold fluid heats from 25 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 115 °CTc: 25 → 50 °C
ΔTlm = K
2.Easy
lengthT100 °C55 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 100 to 55 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 100 → 55 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
3.Medium
lengthT165 °C135 °C90 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 420 kW. The hot fluid cools from 165 to 135 °C and the cold fluid heats from 10 to 90 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 420 kWU = 1000 W/(m²·K)Th: 165 → 135 °CTc: 10 → 90 °C
A = m²
4.Medium
lengthT150 °C120 °C75 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 150 kW. The hot fluid cools from 150 to 120 °C and the cold fluid heats from 25 to 75 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 150 kWU = 300 W/(m²·K)Th: 150 → 120 °CTc: 25 → 75 °C
A = m²
5.Hard
lengthT100 °C55 °C51.91 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 100 to 55 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 100 → 55 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT170 °C150 °C31 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 170 to 150 °C in a counter-flow exchanger. It heats 0.5 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 = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 170 → 150 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 87.64 K
  2. 2. Tc,out = 46.51 °C
  3. 3. A = 4.291 m²
  4. 4. A = 5.91 m²
  5. 5. A = 7.337 m²
  6. 6. A = 0.5702 m²

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