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 °C115 °C95 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 180 to 115 °C while the cold fluid heats from 25 to 95 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 115 °CTc: 25 → 95 °C
ΔTlm = K
2.Easy
lengthT85 °C70 °C30 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 70 °C while the cold fluid heats from 10 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 70 °CTc: 10 → 30 °C
ΔTlm = K
3.Medium
lengthT110 °C30 °C85 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 30 kW. The hot fluid cools from 110 to 30 °C and the cold fluid heats from 10 to 85 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 30 kWU = 300 W/(m²·K)Th: 110 → 30 °CTc: 10 → 85 °C
A = m²
4.Medium
lengthT130 °C10 °C80 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °C on the outside of the tubes. Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 80 °C. The overall heat transfer coefficient is 2500 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 80 °CU = 2500 W/(m²·K)
A = m²
5.Hard
lengthT115 °C50 °C21.48 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 115 to 50 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °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: 115 → 50 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT170 °C90 °C98.04 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 170 to 90 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 170 → 90 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 87.48 K
  2. 2. ΔTlm = 57.46 K
  3. 3. A = 4.463 m²
  4. 4. A = 2.928 m²
  5. 5. A = 6.823 m²
  6. 6. A = 4.848 m²

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