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
lengthT95 °C55 °C80 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 55 °C while the cold fluid heats from 25 to 80 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 55 °CTc: 25 → 80 °C
ΔTlm = K
2.Easy
lengthT120 °C85 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 85 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 85 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
3.Medium
lengthT150 °C80 °C25 °C70 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 250 kW. Its heat transfer area is 2 m². The hot fluid cools from 150 to 80 °C and the cold fluid heats from 25 to 70 °C. Find the overall heat transfer coefficient U.

Q̇ = 250 kWA = 2 m²Th: 150 → 80 °CTc: 25 → 70 °C
U = W/(m²·K)
4.Medium
lengthT175 °C160 °C125 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 700 kW. The hot fluid cools from 175 to 160 °C and the cold fluid heats from 10 to 125 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 700 kWF = 0.92U = 1000 W/(m²·K)Th: 175 → 160 °CTc: 10 → 125 °C
A = m²
5.Hard
lengthT170 °C85 °C67.7 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 170 to 85 °C in a counter-flow exchanger. It heats 0.5 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 = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 170 → 85 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT95 °C40 °C26.91 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 95 to 40 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 95 → 40 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 21.64 K
  2. 2. Tc,out = 33.49 °C
  3. 3. U = 2745 W/(m²·K)
  4. 4. A = 8.359 m²
  5. 5. A = 1.407 m²
  6. 6. A = 1.471 m²

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