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 °C120 °C10 °C110 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 175 to 120 °C while the cold fluid heats from 10 to 110 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 120 °CTc: 10 → 110 °C
ΔTlm = K
2.Easy
lengthT105 °C50 °C55 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 105 to 50 °C while the cold fluid heats from 10 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 50 °CTc: 10 → 55 °C
ΔTlm = K
3.Medium
lengthT100 °C35 °C55 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 470 kW. The hot fluid cools from 100 to 35 °C and the cold fluid heats from 15 to 55 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 470 kWU = 500 W/(m²·K)Th: 100 → 35 °CTc: 15 → 55 °C
A = m²
4.Medium
lengthT115 °C80 °C15 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 290 kW. The hot fluid cools from 115 to 80 °C and the cold fluid heats from 15 to 45 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 290 kWU = 300 W/(m²·K)Th: 115 → 80 °CTc: 15 → 45 °C
A = m²
5.Hard
lengthT100 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 100 °C on the outside of the tubes of a condenser with a heat transfer area of 5 m² and U = 1000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 5 m²U = 1000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT170 °C140 °C42.01 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 170 to 140 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 170 → 140 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 55.29 K
  2. 2. ΔTlm = 44.81 K
  3. 3. A = 30.49 m²
  4. 4. A = 15.61 m²
  5. 5. Tc,out = 46.31 °C
  6. 6. A = 5.567 m²

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