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
lengthT125 °C80 °C10 °C20 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 125 to 80 °C while the cold fluid heats from 10 to 20 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 80 °CTc: 10 → 20 °C
ΔTlm = K
2.Easy
lengthT100 °C55 °C?15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 100 to 55 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 100 → 55 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
3.Medium
lengthT80 °C45 °C20 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 480 kW. Its heat transfer area is 15 m². The hot fluid cools from 80 to 45 °C and the cold fluid heats from 20 to 30 °C. Find the overall heat transfer coefficient U.

Q̇ = 480 kWA = 15 m²Th: 80 → 45 °CTc: 20 → 30 °C
U = W/(m²·K)
4.Medium
lengthT100 °C20 °C55 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °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 20 to 55 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 55 °CU = 1500 W/(m²·K)
A = m²
5.Hard
lengthT95 °C55 °C40.95 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 95 to 55 °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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 95 → 55 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT120 °C100 °C43.92 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 100 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 100 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 84.54 K
  2. 2. Tc,out = 68.83 °C
  3. 3. U = 985.8 W/(m²·K)
  4. 4. A = 4.81 m²
  5. 5. A = 6.12 m²
  6. 6. A = 2.563 m²

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