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
lengthT80 °C55 °C25 °C50 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 80 to 55 °C while the cold fluid heats from 25 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 80 → 55 °CTc: 25 → 50 °C
ΔTlm = K
2.Easy
lengthT105 °C40 °C95 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 20 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 105 to 40 °C and the cold fluid heats from 25 to 95 °C. Find the heat transfer rate Q̇.

A = 20 m²U = 800 W/(m²·K)Th: 105 → 40 °CTc: 25 → 95 °C
Q̇ = kW
3.Medium
lengthT140 °C20 °C60 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °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 20 to 60 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 60 °CU = 1000 W/(m²·K)
A = m²
4.Medium
lengthT80 °C50 °C20 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 500 kW. The hot fluid cools from 80 to 50 °C and the cold fluid heats from 20 to 45 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 500 kWU = 500 W/(m²·K)Th: 80 → 50 °CTc: 20 → 45 °C
A = m²
5.Hard
lengthT155 °C120 °C42.58 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 120 °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 = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 120 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT140 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 140 °C on the outside of the tubes of a condenser with a heat transfer area of 1.5 m² and U = 2000 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 1.5 m²U = 2000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 20.85 K
  2. 2. Q̇ = 197.3 kW
  3. 3. A = 8.474 m²
  4. 4. A = 45.18 m²
  5. 5. A = 3.552 m²
  6. 6. Tc,out = 65.63 °C

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