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 °C40 °C50 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 40 °C while the cold fluid heats from 20 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 40 °CTc: 20 → 50 °C
ΔTlm = K
2.Easy
lengthT85 °C50 °C45 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 50 °C while the cold fluid heats from 25 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 50 °CTc: 25 → 45 °C
ΔTlm = K
3.Medium
lengthT155 °C100 °C140 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 370 kW. Its heat transfer area is 8 m². The hot fluid cools from 155 to 100 °C and the cold fluid heats from 15 to 140 °C. Find the overall heat transfer coefficient U.

Q̇ = 370 kWA = 8 m²Th: 155 → 100 °CTc: 15 → 140 °C
U = W/(m²·K)
4.Medium
lengthT160 °C110 °C115 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 400 kW. Its heat transfer area is 25 m². The hot fluid cools from 160 to 110 °C and the cold fluid heats from 30 to 115 °C. Find the overall heat transfer coefficient U.

Q̇ = 400 kWA = 25 m²Th: 160 → 110 °CTc: 30 → 115 °C
U = W/(m²·K)
5.Hard
lengthT105 °C??25 °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 105 °C and the cold stream at 25 °C. The exchanger has A = 2 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 105 °CTc,in = 25 °CA = 2 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT160 °C60 °C63.49 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 160 to 60 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 160 → 60 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 44.92 K
  2. 2. ΔTlm = 31.91 K
  3. 3. U = 1146 W/(m²·K)
  4. 4. U = 263 W/(m²·K)
  5. 5. Th,out = 63.71 °C
  6. 6. A = 3.689 m²

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