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
lengthT90 °C35 °C25 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 35 °C while the cold fluid heats from 10 to 25 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 35 °CTc: 10 → 25 °C
ΔTlm = K
2.Easy
lengthT130 °C55 °C75 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 55 °C while the cold fluid heats from 25 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 55 °CTc: 25 → 75 °C
ΔTlm = K
3.Medium
lengthT130 °C25 °C80 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °C on the outside of the tubes. Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 25 to 80 °C. The overall heat transfer coefficient is 2500 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 80 °CU = 2500 W/(m²·K)
A = m²
4.Medium
lengthT170 °C90 °C150 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 30 kW. The hot fluid cools from 170 to 90 °C and the cold fluid heats from 25 to 150 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 30 kWU = 200 W/(m²·K)Th: 170 → 90 °CTc: 25 → 150 °C
A = m²
5.Hard
lengthT95 °C75 °C42.94 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 95 to 75 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 95 → 75 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT85 °C65 °C74.02 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 85 to 65 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 85 → 65 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 41.86 K
  2. 2. ΔTlm = 41.24 K
  3. 3. A = 1.241 m²
  4. 4. A = 3.929 m²
  5. 5. A = 2.94 m²
  6. 6. A = 14.8 m²

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