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
lengthT150 °C105 °C115 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 150 to 105 °C while the cold fluid heats from 30 to 115 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 105 °CTc: 30 → 115 °C
ΔTlm = K
2.Easy
lengthT170 °C145 °C150 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 170 to 145 °C while the cold fluid heats from 20 to 150 °C. Find the log-mean temperature difference ΔTlm.

Th: 170 → 145 °CTc: 20 → 150 °C
ΔTlm = K
3.Medium
lengthT175 °C155 °C10 °C70 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 20 kW. The hot fluid cools from 175 to 155 °C and the cold fluid heats from 10 to 70 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 20 kWU = 200 W/(m²·K)Th: 175 → 155 °CTc: 10 → 70 °C
A = m²
4.Medium
lengthT155 °C40 °C50 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 150 kW. The hot fluid cools from 155 to 40 °C and the cold fluid heats from 15 to 50 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 150 kWF = 0.88U = 500 W/(m²·K)Th: 155 → 40 °CTc: 15 → 50 °C
A = m²
5.Hard
lengthT105 °C50 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 105 to 50 °C. Water (1 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 25 mm, and U = 400 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 105 → 50 °Cṁc = 1 kg/sTc,in = 10 °CD = 25 mmU = 400 W/(m²·K)
L = m
6.Hard
lengthT95 °C60 °C27.84 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 95 to 60 °C in a counter-flow exchanger. It heats 1.5 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 = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 95 → 60 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 52.48 K
  2. 2. ΔTlm = 57.3 K
  3. 3. A = 0.8291 m²
  4. 4. A = 6.115 m²
  5. 5. L = 18.27 m
  6. 6. A = 1.455 m²

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