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
lengthT110 °C55 °C25 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 110 to 55 °C while the cold fluid heats from 10 to 25 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 55 °CTc: 10 → 25 °C
ΔTlm = K
2.Easy
lengthT180 °C85 °C85 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 180 to 85 °C while the cold fluid heats from 25 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 85 °CTc: 25 → 85 °C
ΔTlm = K
3.Medium
lengthT130 °C65 °C40 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 50 kW. The hot fluid cools from 130 to 65 °C and the cold fluid heats from 25 to 40 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 50 kWU = 1000 W/(m²·K)Th: 130 → 65 °CTc: 25 → 40 °C
A = m²
4.Medium
lengthT180 °C70 °C155 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 290 kW. The hot fluid cools from 180 to 70 °C and the cold fluid heats from 20 to 155 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 290 kWF = 0.9U = 300 W/(m²·K)Th: 180 → 70 °CTc: 20 → 155 °C
A = m²
5.Hard
lengthT160 °C115 °C20 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 160 to 115 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °C. The inner tube has a diameter of 50 mm, and U = 150 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 160 → 115 °Cṁc = 0.5 kg/sTc,in = 20 °CD = 50 mmU = 150 W/(m²·K)
L = m
6.Hard
lengthT180 °C95 °C52.7 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 180 to 95 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 180 → 95 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 62.89 K
  2. 2. ΔTlm = 76.16 K
  3. 3. A = 0.8109 m²
  4. 4. A = 29.78 m²
  5. 5. L = 45.97 m
  6. 6. A = 1.704 m²

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