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
lengthT140 °C115 °C30 °C85 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 140 to 115 °C while the cold fluid heats from 30 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 115 °CTc: 30 → 85 °C
ΔTlm = K
2.Easy
lengthT105 °C80 °C20 °C60 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 105 to 80 °C while the cold fluid heats from 20 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 80 °CTc: 20 → 60 °C
ΔTlm = K
3.Medium
lengthT105 °C15 °C50 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 105 °C on the outside of the tubes. Cooling water (5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 15 to 50 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 105 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 15 → 50 °CU = 1500 W/(m²·K)
A = m²
4.Medium
lengthT100 °C60 °C65 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 370 kW. The hot fluid cools from 100 to 60 °C and the cold fluid heats from 10 to 65 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 370 kWU = 300 W/(m²·K)Th: 100 → 60 °CTc: 10 → 65 °C
A = m²
5.Hard
lengthT110 °C60 °C39.95 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 110 to 60 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 110 → 60 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT105 °C65 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-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 105 to 65 °C. Water (1 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: 105 → 65 °Cṁc = 1 kg/sTc,in = 15 °CD = 40 mmU = 400 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 61.57 K
  2. 2. ΔTlm = 44.92 K
  3. 3. A = 6.862 m²
  4. 4. A = 29.33 m²
  5. 5. A = 2.475 m²
  6. 6. L = 8.411 m

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