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
lengthT175 °C40 °C45 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 40 °C while the cold fluid heats from 20 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 40 °CTc: 20 → 45 °C
ΔTlm = K
2.Easy
lengthT135 °C100 °C70 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 5 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 135 to 100 °C and the cold fluid heats from 20 to 70 °C. Find the heat transfer rate Q̇.

A = 5 m²U = 300 W/(m²·K)Th: 135 → 100 °CTc: 20 → 70 °C
Q̇ = kW
3.Medium
lengthT100 °C10 °C90 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 90 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 90 °CU = 3000 W/(m²·K)
A = m²
4.Medium
lengthT80 °C40 °C70 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 70 kW. The hot fluid cools from 80 to 40 °C and the cold fluid heats from 25 to 70 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 70 kWU = 1000 W/(m²·K)Th: 80 → 40 °CTc: 25 → 70 °C
A = m²
5.Hard
lengthT140 °C105 °C34.63 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 140 to 105 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 140 → 105 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT115 °C55 °C21.96 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 115 to 55 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 115 → 55 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 58.77 K
  2. 2. Q̇ = 108.4 kW
  3. 3. A = 4.592 m²
  4. 4. A = 5.677 m²
  5. 5. A = 0.874 m²
  6. 6. A = 1.418 m²

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