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
lengthT180 °C115 °C165 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 5 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 180 to 115 °C and the cold fluid heats from 25 to 165 °C. Find the heat transfer rate Q̇.

A = 5 m²U = 800 W/(m²·K)Th: 180 → 115 °CTc: 25 → 165 °C
Q̇ = kW
2.Easy
lengthT135 °C70 °C90 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 70 °C while the cold fluid heats from 30 to 90 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 70 °CTc: 30 → 90 °C
ΔTlm = K
3.Medium
lengthT115 °C50 °C80 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 380 kW. The hot fluid cools from 115 to 50 °C and the cold fluid heats from 10 to 80 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 380 kWU = 800 W/(m²·K)Th: 115 → 50 °CTc: 10 → 80 °C
A = m²
4.Medium
lengthT120 °C90 °C105 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 290 kW. The hot fluid cools from 120 to 90 °C and the cold fluid heats from 20 to 105 °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: 120 → 90 °CTc: 20 → 105 °C
A = m²
5.Hard
lengthT110 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 110 °C on the outside of the tubes of a condenser with a heat transfer area of 3 m² and U = 1000 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 3 m²U = 1000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT150 °C??25 °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 25 °C. The exchanger has A = 4 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 4 kW/KTh,in = 150 °CTc,in = 25 °CA = 4 m²U = 300 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 167.4 kW
  2. 2. ΔTlm = 42.45 K
  3. 3. A = 12.69 m²
  4. 4. A = 27.07 m²
  5. 5. Tc,out = 66.09 °C
  6. 6. Th,out = 121.2 °C

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