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 °C100 °C70 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 100 °C while the cold fluid heats from 15 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 100 °CTc: 15 → 70 °C
ΔTlm = K
2.Easy
lengthT145 °C100 °C100 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 145 to 100 °C while the cold fluid heats from 25 to 100 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 100 °CTc: 25 → 100 °C
ΔTlm = K
3.Medium
lengthT150 °C80 °C10 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 330 kW. Its heat transfer area is 1 m². The hot fluid cools from 150 to 80 °C and the cold fluid heats from 10 to 30 °C. Find the overall heat transfer coefficient U.

Q̇ = 330 kWA = 1 m²Th: 150 → 80 °CTc: 10 → 30 °C
U = W/(m²·K)
4.Medium
lengthT170 °C120 °C15 °C25 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 460 kW. Its heat transfer area is 25 m². The hot fluid cools from 170 to 120 °C and the cold fluid heats from 15 to 25 °C. Find the overall heat transfer coefficient U.

Q̇ = 460 kWA = 25 m²Th: 170 → 120 °CTc: 15 → 25 °C
U = W/(m²·K)
5.Hard
lengthT115 °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 115 °C and the cold stream at 25 °C. The exchanger has A = 5 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 115 °CTc,in = 25 °CA = 5 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT100 °C70 °C35.98 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 100 to 70 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 100 → 70 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 87.48 K
  2. 2. ΔTlm = 58.73 K
  3. 3. U = 3775 W/(m²·K)
  4. 4. U = 150.1 W/(m²·K)
  5. 5. Th,out = 65 °C
  6. 6. A = 0.979 m²

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