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
lengthT80 °C30 °C45 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 80 to 30 °C while the cold fluid heats from 10 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 80 → 30 °CTc: 10 → 45 °C
ΔTlm = K
2.Easy
lengthT90 °C70 °C20 °C30 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 70 °C while the cold fluid heats from 20 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 70 °CTc: 20 → 30 °C
ΔTlm = K
3.Medium
lengthT170 °C95 °C20 °C85 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 40 kW. The hot fluid cools from 170 to 95 °C and the cold fluid heats from 20 to 85 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 40 kWU = 1000 W/(m²·K)Th: 170 → 95 °CTc: 20 → 85 °C
A = m²
4.Medium
lengthT180 °C60 °C75 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 150 kW. The hot fluid cools from 180 to 60 °C and the cold fluid heats from 30 to 75 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 150 kWU = 800 W/(m²·K)Th: 180 → 60 °CTc: 30 → 75 °C
A = m²
5.Hard
lengthT140 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 140 °C and the cold stream at 25 °C. The exchanger has A = 3 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 140 °CTc,in = 25 °CA = 3 m²U = 200 W/(m²·K)
Th,out = °C
6.Hard
lengthT140 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 140 °C on the outside of the tubes of a condenser with a heat transfer area of 2.5 m² and U = 3000 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 = 140 °CA = 2.5 m²U = 3000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 26.8 K
  2. 2. ΔTlm = 53.61 K
  3. 3. A = 0.7737 m²
  4. 4. A = 3.132 m²
  5. 5. Th,out = 107.1 °C
  6. 6. Tc,out = 74.02 °C

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