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
lengthT90 °C30 °C40 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 30 °C while the cold fluid heats from 15 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 30 °CTc: 15 → 40 °C
ΔTlm = K
2.Easy
lengthT130 °C85 °C65 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 85 °C while the cold fluid heats from 25 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 85 °CTc: 25 → 65 °C
ΔTlm = K
3.Medium
lengthT105 °C70 °C15 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 390 kW. Its heat transfer area is 10 m². The hot fluid cools from 105 to 70 °C and the cold fluid heats from 15 to 50 °C. Find the overall heat transfer coefficient U.

Q̇ = 390 kWA = 10 m²Th: 105 → 70 °CTc: 15 → 50 °C
U = W/(m²·K)
4.Medium
lengthT115 °C60 °C85 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 340 kW. Its heat transfer area is 8 m². The hot fluid cools from 115 to 60 °C and the cold fluid heats from 10 to 85 °C. Find the overall heat transfer coefficient U.

Q̇ = 340 kWA = 8 m²Th: 115 → 60 °CTc: 10 → 85 °C
U = W/(m²·K)
5.Hard
lengthT160 °C??30 °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 160 °C and the cold stream at 30 °C. The exchanger has A = 5 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 160 °CTc,in = 30 °CA = 5 m²U = 200 W/(m²·K)
Th,out = °C
6.Hard
lengthT115 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 115 °C and the cold stream at 15 °C. The exchanger has A = 1 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 115 °CTc,in = 15 °CA = 1 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 29.07 K
  2. 2. ΔTlm = 62.47 K
  3. 3. U = 838 W/(m²·K)
  4. 4. U = 1086 W/(m²·K)
  5. 5. Th,out = 73.33 °C
  6. 6. Th,out = 90 °C

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