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
lengthT160 °C140 °C45 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 140 °C while the cold fluid heats from 30 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 140 °CTc: 30 → 45 °C
ΔTlm = K
2.Easy
lengthT155 °C75 °C70 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2.5 m² and an overall heat transfer coefficient of 200 W/(m²·K). The hot fluid cools from 155 to 75 °C and the cold fluid heats from 25 to 70 °C. Find the heat transfer rate Q̇.

A = 2.5 m²U = 200 W/(m²·K)Th: 155 → 75 °CTc: 25 → 70 °C
Q̇ = kW
3.Medium
lengthT150 °C60 °C70 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 280 kW. The hot fluid cools from 150 to 60 °C and the cold fluid heats from 30 to 70 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 280 kWF = 0.95U = 1000 W/(m²·K)Th: 150 → 60 °CTc: 30 → 70 °C
A = m²
4.Medium
lengthT125 °C40 °C35 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 130 kW. The hot fluid cools from 125 to 40 °C and the cold fluid heats from 20 to 35 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 130 kWU = 300 W/(m²·K)Th: 125 → 40 °CTc: 20 → 35 °C
A = m²
5.Hard
lengthT145 °C80 °C15 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 145 to 80 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 40 mm, and U = 400 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.3 kJ/(kg·K)Th: 145 → 80 °Cṁc = 1.5 kg/sTc,in = 15 °CD = 40 mmU = 400 W/(m²·K)
L = m
6.Hard
lengthT155 °C50 °C67.75 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 50 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 50 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 112.5 K
  2. 2. Q̇ = 32.98 kW
  3. 3. A = 5.782 m²
  4. 4. A = 9.311 m²
  5. 5. L = 10.01 m
  6. 6. A = 12.85 m²

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