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
lengthT100 °C55 °C60 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 100 to 55 °C while the cold fluid heats from 25 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 100 → 55 °CTc: 25 → 60 °C
ΔTlm = K
2.Easy
lengthT110 °C45 °C95 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 110 to 45 °C while the cold fluid heats from 25 to 95 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 45 °CTc: 25 → 95 °C
ΔTlm = K
3.Medium
lengthT130 °C95 °C45 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 100 kW. The hot fluid cools from 130 to 95 °C and the cold fluid heats from 15 to 45 °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: 130 → 95 °CTc: 15 → 45 °C
A = m²
4.Medium
lengthT160 °C100 °C15 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 300 kW. The hot fluid cools from 160 to 100 °C and the cold fluid heats from 15 to 40 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 300 W/(m²·K)Th: 160 → 100 °CTc: 15 → 40 °C
A = m²
5.Hard
lengthT105 °C25 °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 = 1000 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 8 m²U = 1000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT175 °C??30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 3 kW/K. The hot stream enters at 175 °C and the cold stream at 30 °C. The exchanger has A = 2 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 3 kW/KTh,in = 175 °CTc,in = 30 °CA = 2 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 34.76 K
  2. 2. ΔTlm = 17.38 K
  3. 3. A = 1.516 m²
  4. 4. A = 10.38 m²
  5. 5. Tc,out = 82.67 °C
  6. 6. Th,out = 138.8 °C

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