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
lengthT150 °C125 °C30 °C60 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 150 to 125 °C while the cold fluid heats from 30 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 125 °CTc: 30 → 60 °C
ΔTlm = K
2.Easy
lengthT115 °C70 °C60 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 70 °C while the cold fluid heats from 25 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 70 °CTc: 25 → 60 °C
ΔTlm = K
3.Medium
lengthT155 °C115 °C80 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 470 kW. The hot fluid cools from 155 to 115 °C and the cold fluid heats from 15 to 80 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 470 kWU = 300 W/(m²·K)Th: 155 → 115 °CTc: 15 → 80 °C
A = m²
4.Medium
lengthT130 °C30 °C75 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °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 30 to 75 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc: 30 → 75 °CU = 3500 W/(m²·K)
A = m²
5.Hard
lengthT180 °C140 °C86.77 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 180 to 140 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 180 → 140 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT155 °C135 °C40.05 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 135 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 135 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 89.71 K
  2. 2. ΔTlm = 49.83 K
  3. 3. A = 18.03 m²
  4. 4. A = 1.071 m²
  5. 5. A = 0.923 m²
  6. 6. A = 0.5732 m²

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