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
lengthT130 °C70 °C10 °C40 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 130 to 70 °C while the cold fluid heats from 10 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 70 °CTc: 10 → 40 °C
ΔTlm = K
2.Easy

In a heat exchanger 2 kg/s of ethanol (cp = 2.44 kJ/(kg·K)) is cooled from 60 to 40 °C. Find the heat transfer rate Q̇.

ṁ = 2 kg/scp = 2.44 kJ/(kg·K)T: 60 → 40 °C
Q̇ = kW
3.Medium
lengthT90 °C65 °C25 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 450 kW. The hot fluid cools from 90 to 65 °C and the cold fluid heats from 10 to 25 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 450 kWF = 0.92U = 800 W/(m²·K)Th: 90 → 65 °CTc: 10 → 25 °C
A = m²
4.Medium
lengthT125 °C100 °C85 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 300 kW. Its heat transfer area is 2 m². The hot fluid cools from 125 to 100 °C and the cold fluid heats from 25 to 85 °C. Find the overall heat transfer coefficient U.

Q̇ = 300 kWA = 2 m²Th: 125 → 100 °CTc: 25 → 85 °C
U = W/(m²·K)
5.Hard
lengthT150 °C75 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 150 to 75 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 50 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 150 → 75 °Cṁc = 0.5 kg/sTc,in = 15 °CD = 50 mmU = 500 W/(m²·K)
L = m
6.Hard
lengthT150 °C100 °C30.63 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 150 to 100 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 150 → 100 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 64.92 K
  2. 2. Q̇ = 97.6 kW
  3. 3. A = 10.21 m²
  4. 4. U = 2694 W/(m²·K)
  5. 5. L = 45.65 m
  6. 6. A = 3.318 m²

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