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 °C60 °C100 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 60 °C while the cold fluid heats from 10 to 100 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 60 °CTc: 10 → 100 °C
ΔTlm = K
2.Easy

In a heat exchanger 0.8 kg/s of water (cp = 4.18 kJ/(kg·K)) is cooled from 65 to 25 °C. Find the heat transfer rate Q̇.

ṁ = 0.8 kg/scp = 4.18 kJ/(kg·K)T: 65 → 25 °C
Q̇ = kW
3.Medium
lengthT140 °C115 °C15 °C75 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 170 kW. Its heat transfer area is 3 m². The hot fluid cools from 140 to 115 °C and the cold fluid heats from 15 to 75 °C. Find the overall heat transfer coefficient U.

Q̇ = 170 kWA = 3 m²Th: 140 → 115 °CTc: 15 → 75 °C
U = W/(m²·K)
4.Medium
lengthT105 °C65 °C20 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 390 kW. The hot fluid cools from 105 to 65 °C and the cold fluid heats from 20 to 50 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWU = 1000 W/(m²·K)Th: 105 → 65 °CTc: 20 → 50 °C
A = m²
5.Hard
lengthT90 °C65 °C27.56 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 90 to 65 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 90 → 65 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT155 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 155 °C and the cold stream at 25 °C. The exchanger has A = 5 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 155 °CTc,in = 25 °CA = 5 m²U = 800 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 54.85 K
  2. 2. Q̇ = 133.8 kW
  3. 3. U = 759.6 W/(m²·K)
  4. 4. A = 9.664 m²
  5. 5. A = 1.875 m²
  6. 6. Th,out = 68.33 °C

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