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
lengthT135 °C115 °C75 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 115 °C while the cold fluid heats from 20 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 115 °CTc: 20 → 75 °C
ΔTlm = K
2.Easy
lengthT140 °C30 °C30 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 140 to 30 °C while the cold fluid heats from 10 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 30 °CTc: 10 → 30 °C
ΔTlm = K
3.Medium
lengthT175 °C70 °C105 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 590 kW. The hot fluid cools from 175 to 70 °C and the cold fluid heats from 20 to 105 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 590 kWF = 0.92U = 1000 W/(m²·K)Th: 175 → 70 °CTc: 20 → 105 °C
A = m²
4.Medium
lengthT160 °C130 °C10 °C85 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 300 kW. The hot fluid cools from 160 to 130 °C and the cold fluid heats from 10 to 85 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 300 W/(m²·K)Th: 160 → 130 °CTc: 10 → 85 °C
A = m²
5.Hard
lengthT160 °C??10 °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 10 °C. The exchanger has A = 1.5 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 160 °CTc,in = 10 °CA = 1.5 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT180 °C??20 °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 180 °C and the cold stream at 20 °C. The exchanger has A = 3 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 180 °CTc,in = 20 °CA = 3 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 76.16 K
  2. 2. ΔTlm = 52.79 K
  3. 3. A = 10.79 m²
  4. 4. A = 11.47 m²
  5. 5. Th,out = 54.12 °C
  6. 6. Th,out = 100 °C

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