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
lengthT120 °C30 °C40 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 30 °C while the cold fluid heats from 15 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 30 °CTc: 15 → 40 °C
ΔTlm = K
2.Easy
lengthT135 °C90 °C110 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 90 °C while the cold fluid heats from 15 to 110 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 90 °CTc: 15 → 110 °C
ΔTlm = K
3.Medium
lengthT110 °C10 °C25 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 110 °C on the outside of the tubes. Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 25 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 110 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 25 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT95 °C60 °C15 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 180 kW. Its heat transfer area is 6 m². The hot fluid cools from 95 to 60 °C and the cold fluid heats from 15 to 30 °C. Find the overall heat transfer coefficient U.

Q̇ = 180 kWA = 6 m²Th: 95 → 60 °CTc: 15 → 30 °C
U = W/(m²·K)
5.Hard
lengthT140 °C55 °C58.89 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 140 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 25 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 140 → 55 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT100 °C60 °C20.5 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 100 to 60 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 100 → 60 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 38.83 K
  2. 2. ΔTlm = 45.51 K
  3. 3. A = 0.5823 m²
  4. 4. U = 588.5 W/(m²·K)
  5. 5. A = 8.271 m²
  6. 6. A = 0.7588 m²

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