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 °C115 °C165 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 115 °C while the cold fluid heats from 20 to 165 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 115 °CTc: 20 → 165 °C
ΔTlm = K
2.Easy

In a heat exchanger 0.5 kg/s of glycol mix (cp = 3.6 kJ/(kg·K)) is heated from 30 to 75 °C. Find the heat transfer rate Q̇.

ṁ = 0.5 kg/scp = 3.6 kJ/(kg·K)T: 30 → 75 °C
Q̇ = kW
3.Medium
lengthT95 °C70 °C45 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 470 kW. The hot fluid cools from 95 to 70 °C and the cold fluid heats from 30 to 45 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 470 kWU = 200 W/(m²·K)Th: 95 → 70 °CTc: 30 → 45 °C
A = m²
4.Medium
lengthT130 °C115 °C25 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 280 kW. Its heat transfer area is 2 m². The hot fluid cools from 130 to 115 °C and the cold fluid heats from 25 to 50 °C. Find the overall heat transfer coefficient U.

Q̇ = 280 kWA = 2 m²Th: 130 → 115 °CTc: 25 → 50 °C
U = W/(m²·K)
5.Hard
lengthT110 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 110 °C on the outside of the tubes of a condenser with a heat transfer area of 1 m² and U = 3000 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 1 m²U = 3000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT140 °C45 °C33.71 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 140 to 45 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 140 → 45 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 37.76 K
  2. 2. Q̇ = 81 kW
  3. 3. A = 52.44 m²
  4. 4. U = 1679 W/(m²·K)
  5. 5. Tc,out = 68.53 °C
  6. 6. A = 2.644 m²

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