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
lengthT180 °C70 °C10 °C30 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 180 to 70 °C while the cold fluid heats from 10 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 70 °CTc: 10 → 30 °C
ΔTlm = K
2.Easy
lengthT95 °C65 °C85 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 65 °C while the cold fluid heats from 25 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 65 °CTc: 25 → 85 °C
ΔTlm = K
3.Medium
lengthT120 °C100 °C25 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 140 kW. The hot fluid cools from 120 to 100 °C and the cold fluid heats from 25 to 60 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 140 kWU = 300 W/(m²·K)Th: 120 → 100 °CTc: 25 → 60 °C
A = m²
4.Medium
lengthT135 °C75 °C15 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 240 kW. Its heat transfer area is 3 m². The hot fluid cools from 135 to 75 °C and the cold fluid heats from 15 to 30 °C. Find the overall heat transfer coefficient U.

Q̇ = 240 kWA = 3 m²Th: 135 → 75 °CTc: 15 → 30 °C
U = W/(m²·K)
5.Hard
lengthT80 °C45 °C25.47 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 80 to 45 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 80 → 45 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT120 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 120 °C on the outside of the tubes of a condenser with a heat transfer area of 5 m² and U = 1000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 120 °CA = 5 m²U = 1000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 89.85 K
  2. 2. ΔTlm = 21.64 K
  3. 3. A = 7.339 m²
  4. 4. U = 1046 W/(m²·K)
  5. 5. A = 3.552 m²
  6. 6. Tc,out = 52.88 °C

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