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 °C85 °C15 °C25 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 175 to 85 °C while the cold fluid heats from 15 to 25 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 85 °CTc: 15 → 25 °C
ΔTlm = K
2.Easy
lengthT110 °C55 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 110 to 55 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 110 → 55 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
3.Medium
lengthT90 °C45 °C70 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 370 kW. The hot fluid cools from 90 to 45 °C and the cold fluid heats from 20 to 70 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 370 kWU = 800 W/(m²·K)Th: 90 → 45 °CTc: 20 → 70 °C
A = m²
4.Medium
lengthT170 °C85 °C20 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 430 kW. The hot fluid cools from 170 to 85 °C and the cold fluid heats from 20 to 60 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 430 kWU = 300 W/(m²·K)Th: 170 → 85 °CTc: 20 → 60 °C
A = m²
5.Hard
lengthT105 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 105 °C on the outside of the tubes of a condenser with a heat transfer area of 1 m² and U = 1000 W/(m²·K). Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 1 m²U = 1000 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT125 °C80 °C45.14 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 125 to 80 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 125 → 80 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 102 K
  2. 2. Tc,out = 66.84 °C
  3. 3. A = 20.64 m²
  4. 4. A = 20.55 m²
  5. 5. Tc,out = 55.42 °C
  6. 6. A = 8.729 m²

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