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
lengthT160 °C65 °C125 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 160 to 65 °C and the cold fluid heats from 20 to 125 °C. Find the heat transfer rate Q̇.

A = 1 m²U = 1500 W/(m²·K)Th: 160 → 65 °CTc: 20 → 125 °C
Q̇ = kW
2.Easy
lengthT85 °C45 °C60 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 45 °C while the cold fluid heats from 15 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 45 °CTc: 15 → 60 °C
ΔTlm = K
3.Medium
lengthT125 °C25 °C10 °C20 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 300 kW. The hot fluid cools from 125 to 25 °C and the cold fluid heats from 10 to 20 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 200 W/(m²·K)Th: 125 → 25 °CTc: 10 → 20 °C
A = m²
4.Medium
lengthT80 °C65 °C15 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 90 kW. The hot fluid cools from 80 to 65 °C and the cold fluid heats from 15 to 60 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 90 kWU = 200 W/(m²·K)Th: 80 → 65 °CTc: 15 → 60 °C
A = m²
5.Hard
lengthT80 °C??10 °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 80 °C and the cold stream at 10 °C. The exchanger has A = 1.5 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 80 °CTc,in = 10 °CA = 1.5 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT160 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 160 °C and the cold stream at 25 °C. The exchanger has A = 1 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 160 °CTc,in = 25 °CA = 1 m²U = 800 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 59.69 kW
  2. 2. ΔTlm = 27.42 K
  3. 3. A = 42.76 m²
  4. 4. A = 19.24 m²
  5. 5. Th,out = 56.67 °C
  6. 6. Th,out = 100 °C

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