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
lengthT160 °C60 °C75 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 60 °C while the cold fluid heats from 25 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 60 °CTc: 25 → 75 °C
ΔTlm = K
2.Easy
lengthT155 °C115 °C45 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 115 °C while the cold fluid heats from 15 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 115 °CTc: 15 → 45 °C
ΔTlm = K
3.Medium
lengthT140 °C100 °C50 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 80 kW. The hot fluid cools from 140 to 100 °C and the cold fluid heats from 20 to 50 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 80 kWU = 1500 W/(m²·K)Th: 140 → 100 °CTc: 20 → 50 °C
A = m²
4.Medium
lengthT110 °C10 °C95 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 110 °C on the outside of the tubes. Cooling water (5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 95 °C. The overall heat transfer coefficient is 2500 W/(m²·K). Find the heat transfer area A needed.

Ts = 110 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 95 °CU = 2500 W/(m²·K)
A = m²
5.Hard
lengthT155 °C75 °C78.69 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 155 to 75 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 155 → 75 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 200 W/(m²·K)
A = m²
6.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 2.5 m² and U = 2500 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 2.5 m²U = 2500 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 56.35 K
  2. 2. ΔTlm = 104.9 K
  3. 3. A = 0.6282 m²
  4. 4. A = 15.86 m²
  5. 5. A = 28.28 m²
  6. 6. Tc,out = 73.18 °C

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