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
lengthT155 °C55 °C145 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 55 °C while the cold fluid heats from 10 to 145 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 55 °CTc: 10 → 145 °C
ΔTlm = K
2.Easy
lengthT180 °C130 °C55 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 180 to 130 °C while the cold fluid heats from 10 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 130 °CTc: 10 → 55 °C
ΔTlm = K
3.Medium
lengthT110 °C15 °C85 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 110 °C on the outside of the tubes. Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 15 to 85 °C. The overall heat transfer coefficient is 2500 W/(m²·K). Find the heat transfer area A needed.

Ts = 110 °Cṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc: 15 → 85 °CU = 2500 W/(m²·K)
A = m²
4.Medium
lengthT105 °C85 °C85 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 320 kW. The hot fluid cools from 105 to 85 °C and the cold fluid heats from 15 to 85 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 320 kWU = 1000 W/(m²·K)Th: 105 → 85 °CTc: 15 → 85 °C
A = m²
5.Hard
lengthT85 °C55 °C40.05 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 85 to 55 °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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 85 → 55 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT140 °C10 °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 2 m² and U = 2000 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 10 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 2 m²U = 2000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 23.27 K
  2. 2. ΔTlm = 122.5 K
  3. 3. A = 4.464 m²
  4. 4. A = 8.018 m²
  5. 5. A = 4.632 m²
  6. 6. Tc,out = 90.07 °C

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