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
lengthT80 °C65 °C65 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 80 to 65 °C while the cold fluid heats from 30 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 80 → 65 °CTc: 30 → 65 °C
ΔTlm = K
2.Easy

In a heat exchanger 3 kg/s of water (cp = 4.18 kJ/(kg·K)) is cooled from 120 to 50 °C. Find the heat transfer rate Q̇.

ṁ = 3 kg/scp = 4.18 kJ/(kg·K)T: 120 → 50 °C
Q̇ = kW
3.Medium
lengthT110 °C45 °C90 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 300 kW. The hot fluid cools from 110 to 45 °C and the cold fluid heats from 30 to 90 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 1000 W/(m²·K)Th: 110 → 45 °CTc: 30 → 90 °C
A = m²
4.Medium
lengthT125 °C85 °C15 °C80 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 170 kW. Its heat transfer area is 15 m². The hot fluid cools from 125 to 85 °C and the cold fluid heats from 15 to 80 °C. Find the overall heat transfer coefficient U.

Q̇ = 170 kWA = 15 m²Th: 125 → 85 °CTc: 15 → 80 °C
U = W/(m²·K)
5.Hard
lengthT140 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 140 °C on the outside of the tubes of a condenser with a heat transfer area of 4 m² and U = 1000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 4 m²U = 1000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT150 °C110 °C47.94 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 150 to 110 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 150 → 110 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 23.6 K
  2. 2. Q̇ = 877.8 kW
  3. 3. A = 17.26 m²
  4. 4. U = 333.6 W/(m²·K)
  5. 5. Tc,out = 56.41 °C
  6. 6. A = 8.28 m²

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