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
lengthT100 °C80 °C75 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 100 to 80 °C while the cold fluid heats from 20 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 100 → 80 °CTc: 20 → 75 °C
ΔTlm = K
2.Easy

In a heat exchanger 1 kg/s of glycol mix (cp = 3.6 kJ/(kg·K)) is heated from 30 to 45 °C. Find the heat transfer rate Q̇.

ṁ = 1 kg/scp = 3.6 kJ/(kg·K)T: 30 → 45 °C
Q̇ = kW
3.Medium
lengthT100 °C80 °C20 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 240 kW. Its heat transfer area is 12 m². The hot fluid cools from 100 to 80 °C and the cold fluid heats from 20 to 40 °C. Find the overall heat transfer coefficient U.

Q̇ = 240 kWA = 12 m²Th: 100 → 80 °CTc: 20 → 40 °C
U = W/(m²·K)
4.Medium
lengthT150 °C45 °C75 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 490 kW. The hot fluid cools from 150 to 45 °C and the cold fluid heats from 30 to 75 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 490 kWU = 1000 W/(m²·K)Th: 150 → 45 °CTc: 30 → 75 °C
A = m²
5.Hard
lengthT100 °C??30 °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 30 °C. The exchanger has A = 3 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 3 kW/KTh,in = 100 °CTc,in = 30 °CA = 3 m²U = 300 W/(m²·K)
Th,out = °C
6.Hard
lengthT125 °C55 °C55.17 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 125 to 55 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 125 → 55 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 39.98 K
  2. 2. Q̇ = 54 kW
  3. 3. U = 346.6 W/(m²·K)
  4. 4. A = 13.14 m²
  5. 5. Th,out = 83.85 °C
  6. 6. A = 1.943 m²

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