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
lengthT150 °C35 °C95 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 150 to 35 °C while the cold fluid heats from 10 to 95 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 35 °CTc: 10 → 95 °C
ΔTlm = K
2.Easy

In a heat exchanger 2.5 kg/s of water (cp = 4.18 kJ/(kg·K)) is heated from 10 to 25 °C. Find the heat transfer rate Q̇.

ṁ = 2.5 kg/scp = 4.18 kJ/(kg·K)T: 10 → 25 °C
Q̇ = kW
3.Medium
lengthT135 °C70 °C55 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 470 kW. The hot fluid cools from 135 to 70 °C and the cold fluid heats from 20 to 55 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 470 kWU = 1000 W/(m²·K)Th: 135 → 70 °CTc: 20 → 55 °C
A = m²
4.Medium
lengthT145 °C60 °C80 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 410 kW. The hot fluid cools from 145 to 60 °C and the cold fluid heats from 20 to 80 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 410 kWU = 800 W/(m²·K)Th: 145 → 60 °CTc: 20 → 80 °C
A = m²
5.Hard
lengthT120 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 120 °C on the outside of the tubes of a condenser with a heat transfer area of 4 m² and U = 2500 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 120 °CA = 4 m²U = 2500 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT150 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 4 kW/K. The hot stream enters at 150 °C and the cold stream at 15 °C. The exchanger has A = 6 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 4 kW/KTh,in = 150 °CTc,in = 15 °CA = 6 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 38.05 K
  2. 2. Q̇ = 156.8 kW
  3. 3. A = 7.363 m²
  4. 4. A = 9.953 m²
  5. 5. Tc,out = 111.3 °C
  6. 6. Th,out = 118.8 °C

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