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 °C35 °C30 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 35 °C while the cold fluid heats from 20 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 35 °CTc: 20 → 30 °C
ΔTlm = K
2.Easy
lengthT80 °C35 °C70 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 80 to 35 °C while the cold fluid heats from 20 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 80 → 35 °CTc: 20 → 70 °C
ΔTlm = K
3.Medium
lengthT95 °C40 °C15 °C25 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 60 kW. The hot fluid cools from 95 to 40 °C and the cold fluid heats from 15 to 25 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 60 kWU = 800 W/(m²·K)Th: 95 → 40 °CTc: 15 → 25 °C
A = m²
4.Medium
lengthT110 °C85 °C15 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 110 kW. Its heat transfer area is 8 m². The hot fluid cools from 110 to 85 °C and the cold fluid heats from 15 to 50 °C. Find the overall heat transfer coefficient U.

Q̇ = 110 kWA = 8 m²Th: 110 → 85 °CTc: 15 → 50 °C
U = W/(m²·K)
5.Hard
lengthT150 °C110 °C44.35 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 150 to 110 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 150 → 110 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT120 °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 120 °C and the cold stream at 10 °C. The exchanger has A = 2 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 120 °CTc,in = 10 °CA = 2 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 32.46 K
  2. 2. ΔTlm = 12.33 K
  3. 3. A = 1.932 m²
  4. 4. U = 228.8 W/(m²·K)
  5. 5. A = 9.179 m²
  6. 6. Th,out = 46.67 °C

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