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 °C110 °C135 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 180 to 110 °C while the cold fluid heats from 30 to 135 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 110 °CTc: 30 → 135 °C
ΔTlm = K
2.Easy
lengthT110 °C80 °C50 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 110 to 80 °C while the cold fluid heats from 25 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 80 °CTc: 25 → 50 °C
ΔTlm = K
3.Medium
lengthT80 °C35 °C70 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 440 kW. The hot fluid cools from 80 to 35 °C and the cold fluid heats from 20 to 70 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 440 kWU = 300 W/(m²·K)Th: 80 → 35 °CTc: 20 → 70 °C
A = m²
4.Medium
lengthT130 °C85 °C20 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 50 kW. Its heat transfer area is 4 m². The hot fluid cools from 130 to 85 °C and the cold fluid heats from 10 to 20 °C. Find the overall heat transfer coefficient U.

Q̇ = 50 kWA = 4 m²Th: 130 → 85 °CTc: 10 → 20 °C
U = W/(m²·K)
5.Hard
lengthT105 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 0.5 kW/K. The hot stream enters at 105 °C and the cold stream at 25 °C. The exchanger has A = 1.5 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 105 °CTc,in = 25 °CA = 1.5 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT150 °C75 °C91.9 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 150 to 75 °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 = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 150 → 75 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 60.83 K
  2. 2. ΔTlm = 57.46 K
  3. 3. A = 118.9 m²
  4. 4. U = 136.8 W/(m²·K)
  5. 5. Th,out = 57 °C
  6. 6. A = 25.23 m²

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