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
lengthT135 °C70 °C35 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 70 °C while the cold fluid heats from 10 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 70 °CTc: 10 → 35 °C
ΔTlm = K
2.Easy
lengthT95 °C65 °C35 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 65 °C while the cold fluid heats from 15 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 65 °CTc: 15 → 35 °C
ΔTlm = K
3.Medium
lengthT110 °C55 °C10 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 300 kW. The hot fluid cools from 110 to 55 °C and the cold fluid heats from 10 to 30 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 300 W/(m²·K)Th: 110 → 55 °CTc: 10 → 30 °C
A = m²
4.Medium
lengthT80 °C55 °C65 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 410 kW. Its heat transfer area is 6 m². The hot fluid cools from 80 to 55 °C and the cold fluid heats from 25 to 65 °C. Find the overall heat transfer coefficient U.

Q̇ = 410 kWA = 6 m²Th: 80 → 55 °CTc: 25 → 65 °C
U = W/(m²·K)
5.Hard
lengthT140 °C30 °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 5 m² and U = 1000 W/(m²·K). Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 5 m²U = 1000 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
6.Hard
lengthT155 °C100 °C26.45 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 155 to 100 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °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: 155 → 100 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 78.3 K
  2. 2. ΔTlm = 54.85 K
  3. 3. A = 18.48 m²
  4. 4. U = 3158 W/(m²·K)
  5. 5. Tc,out = 129.9 °C
  6. 6. A = 2.119 m²

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