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
lengthT95 °C60 °C85 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 60 °C while the cold fluid heats from 10 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 60 °CTc: 10 → 85 °C
ΔTlm = K
2.Easy
lengthT165 °C150 °C30 °C95 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 165 to 150 °C while the cold fluid heats from 30 to 95 °C. Find the log-mean temperature difference ΔTlm.

Th: 165 → 150 °CTc: 30 → 95 °C
ΔTlm = K
3.Medium
lengthT110 °C95 °C25 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 240 kW. The hot fluid cools from 110 to 95 °C and the cold fluid heats from 25 to 45 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 240 kWU = 1000 W/(m²·K)Th: 110 → 95 °CTc: 25 → 45 °C
A = m²
4.Medium
lengthT120 °C35 °C95 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 100 kW. The hot fluid cools from 120 to 35 °C and the cold fluid heats from 20 to 95 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 100 kWU = 800 W/(m²·K)Th: 120 → 35 °CTc: 20 → 95 °C
A = m²
5.Hard
lengthT105 °C15 °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 8 m² and U = 2000 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 8 m²U = 2000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
6.Hard
lengthT110 °C55 °C50.35 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 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 10 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 110 → 55 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 24.85 K
  2. 2. ΔTlm = 89.09 K
  3. 3. A = 3.639 m²
  4. 4. A = 6.385 m²
  5. 5. Tc,out = 97.99 °C
  6. 6. A = 6.084 m²

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