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
lengthT145 °C45 °C70 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 145 to 45 °C while the cold fluid heats from 20 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 45 °CTc: 20 → 70 °C
ΔTlm = K
2.Easy
lengthT160 °C90 °C90 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 90 °C while the cold fluid heats from 10 to 90 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 90 °CTc: 10 → 90 °C
ΔTlm = K
3.Medium
lengthT100 °C10 °C50 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 50 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 50 °CU = 1500 W/(m²·K)
A = m²
4.Medium
lengthT180 °C125 °C30 °C115 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 310 kW. The hot fluid cools from 180 to 125 °C and the cold fluid heats from 30 to 115 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 310 kWU = 300 W/(m²·K)Th: 180 → 125 °CTc: 30 → 115 °C
A = m²
5.Hard
lengthT130 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 1 m² and U = 2500 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 = 130 °CA = 1 m²U = 2500 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.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 1 m² and U = 1000 W/(m²·K). Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 1 m²U = 1000 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 45.51 K
  2. 2. ΔTlm = 74.89 K
  3. 3. A = 8.19 m²
  4. 4. A = 19.99 m²
  5. 5. Tc,out = 69.52 °C
  6. 6. Tc,out = 54.22 °C

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