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
lengthT110 °C35 °C80 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 110 to 35 °C while the cold fluid heats from 20 to 80 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 35 °CTc: 20 → 80 °C
ΔTlm = K
2.Easy
lengthT160 °C115 °C90 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 4 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 160 to 115 °C and the cold fluid heats from 15 to 90 °C. Find the heat transfer rate Q̇.

A = 4 m²U = 1500 W/(m²·K)Th: 160 → 115 °CTc: 15 → 90 °C
Q̇ = kW
3.Medium
lengthT95 °C50 °C40 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 300 kW. The hot fluid cools from 95 to 50 °C and the cold fluid heats from 15 to 40 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 800 W/(m²·K)Th: 95 → 50 °CTc: 15 → 40 °C
A = m²
4.Medium
lengthT180 °C110 °C160 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 430 kW. The hot fluid cools from 180 to 110 °C and the cold fluid heats from 15 to 160 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 430 kWU = 200 W/(m²·K)Th: 180 → 110 °CTc: 15 → 160 °C
A = m²
5.Hard
lengthT105 °C70 °C13.21 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 105 to 70 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 105 → 70 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT100 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 3 kW/K. The hot stream enters at 100 °C and the cold stream at 15 °C. The exchanger has A = 4 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 3 kW/KTh,in = 100 °CTc,in = 15 °CA = 4 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 21.64 K
  2. 2. Q̇ = 504.7 kW
  3. 3. A = 8.475 m²
  4. 4. A = 44.67 m²
  5. 5. A = 1.077 m²
  6. 6. Th,out = 66 °C

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