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
lengthT175 °C40 °C80 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 40 °C while the cold fluid heats from 25 to 80 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 40 °CTc: 25 → 80 °C
ΔTlm = K
2.Easy
lengthT155 °C120 °C25 °C35 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 155 to 120 °C while the cold fluid heats from 25 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 120 °CTc: 25 → 35 °C
ΔTlm = K
3.Medium
lengthT90 °C70 °C55 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 160 kW. The hot fluid cools from 90 to 70 °C and the cold fluid heats from 15 to 55 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 160 kWF = 0.9U = 1000 W/(m²·K)Th: 90 → 70 °CTc: 15 → 55 °C
A = m²
4.Medium
lengthT110 °C70 °C55 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 120 kW. The hot fluid cools from 110 to 70 °C and the cold fluid heats from 25 to 55 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 120 kWU = 300 W/(m²·K)Th: 110 → 70 °CTc: 25 → 55 °C
A = m²
5.Hard
lengthT100 °C50 °C42.56 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 100 to 50 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 100 → 50 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT125 °C90 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.2 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 125 to 90 °C. Water (0.3 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 = 300 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.2 kg/scp,h = 2.3 kJ/(kg·K)Th: 125 → 90 °Cṁc = 0.3 kg/sTc,in = 10 °CD = 25 mmU = 300 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 43.34 K
  2. 2. ΔTlm = 105.9 K
  3. 3. A = 4.018 m²
  4. 4. A = 8.027 m²
  5. 5. A = 8.876 m²
  6. 6. L = 7.54 m

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