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
lengthT155 °C45 °C80 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 45 °C while the cold fluid heats from 10 to 80 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 45 °CTc: 10 → 80 °C
ΔTlm = K
2.Easy
lengthT180 °C85 °C30 °C40 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 180 to 85 °C while the cold fluid heats from 30 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 85 °CTc: 30 → 40 °C
ΔTlm = K
3.Medium
lengthT120 °C45 °C95 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 180 kW. The hot fluid cools from 120 to 45 °C and the cold fluid heats from 30 to 95 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 180 kWU = 1000 W/(m²·K)Th: 120 → 45 °CTc: 30 → 95 °C
A = m²
4.Medium
lengthT135 °C80 °C70 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 90 kW. The hot fluid cools from 135 to 80 °C and the cold fluid heats from 20 to 70 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 90 kWU = 500 W/(m²·K)Th: 135 → 80 °CTc: 20 → 70 °C
A = m²
5.Hard
lengthT160 °C115 °C31.73 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 160 to 115 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 160 → 115 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT110 °C15 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 110 °C on the outside of the tubes of a condenser with a heat transfer area of 8 m² and U = 1000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 8 m²U = 1000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 52.48 K
  2. 2. ΔTlm = 87.21 K
  3. 3. A = 9.195 m²
  4. 4. A = 2.882 m²
  5. 5. A = 2.604 m²
  6. 6. Tc,out = 59.8 °C

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