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
lengthT90 °C75 °C15 °C50 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 75 °C while the cold fluid heats from 15 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 75 °CTc: 15 → 50 °C
ΔTlm = K
2.Easy
lengthT105 °C70 °C55 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 105 to 70 °C while the cold fluid heats from 10 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 70 °CTc: 10 → 55 °C
ΔTlm = K
3.Medium
lengthT140 °C120 °C130 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 460 kW. The hot fluid cools from 140 to 120 °C and the cold fluid heats from 25 to 130 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 460 kWU = 1000 W/(m²·K)Th: 140 → 120 °CTc: 25 → 130 °C
A = m²
4.Medium
lengthT170 °C130 °C45 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 250 kW. The hot fluid cools from 170 to 130 °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 = 250 kWU = 200 W/(m²·K)Th: 170 → 130 °CTc: 30 → 45 °C
A = m²
5.Hard
lengthT130 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 6 m² and U = 2500 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 130 °CA = 6 m²U = 2500 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT125 °C85 °C45.07 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 125 to 85 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 125 → 85 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 45.51 K
  2. 2. ΔTlm = 54.85 K
  3. 3. A = 12.18 m²
  4. 4. A = 11.16 m²
  5. 5. Tc,out = 111.7 °C
  6. 6. A = 9.447 m²

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