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
lengthT125 °C55 °C40 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 125 to 55 °C while the cold fluid heats from 20 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 55 °CTc: 20 → 40 °C
ΔTlm = K
2.Easy
lengthT125 °C50 °C75 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 125 to 50 °C while the cold fluid heats from 30 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 50 °CTc: 30 → 75 °C
ΔTlm = K
3.Medium
lengthT115 °C85 °C80 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 230 kW. The hot fluid cools from 115 to 85 °C and the cold fluid heats from 20 to 80 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 230 kWU = 500 W/(m²·K)Th: 115 → 85 °CTc: 20 → 80 °C
A = m²
4.Medium
lengthT150 °C125 °C100 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 130 kW. The hot fluid cools from 150 to 125 °C and the cold fluid heats from 25 to 100 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 130 kWU = 1000 W/(m²·K)Th: 150 → 125 °CTc: 25 → 100 °C
A = m²
5.Hard
lengthT110 °C70 °C10 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 110 to 70 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 50 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.3 kJ/(kg·K)Th: 110 → 70 °Cṁc = 0.5 kg/sTc,in = 10 °CD = 50 mmU = 500 W/(m²·K)
L = m
6.Hard
lengthT140 °C10 °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 3 m² and U = 2500 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 10 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 3 m²U = 2500 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 56.35 K
  2. 2. ΔTlm = 32.74 K
  3. 3. A = 9.492 m²
  4. 4. A = 1.802 m²
  5. 5. L = 5.016 m
  6. 6. Tc,out = 118.4 °C

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