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

In a heat exchanger 2 kg/s of glycol mix (cp = 3.6 kJ/(kg·K)) is cooled from 120 to 100 °C. Find the heat transfer rate Q̇.

ṁ = 2 kg/scp = 3.6 kJ/(kg·K)T: 120 → 100 °C
Q̇ = kW
2.Easy
lengthT170 °C75 °C100 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 170 to 75 °C while the cold fluid heats from 25 to 100 °C. Find the log-mean temperature difference ΔTlm.

Th: 170 → 75 °CTc: 25 → 100 °C
ΔTlm = K
3.Medium
lengthT115 °C35 °C50 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 250 kW. Its heat transfer area is 8 m². The hot fluid cools from 115 to 35 °C and the cold fluid heats from 20 to 50 °C. Find the overall heat transfer coefficient U.

Q̇ = 250 kWA = 8 m²Th: 115 → 35 °CTc: 20 → 50 °C
U = W/(m²·K)
4.Medium
lengthT110 °C10 °C45 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 110 °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 45 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 110 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 45 °CU = 3500 W/(m²·K)
A = m²
5.Hard
lengthT160 °C120 °C26 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 160 to 120 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 160 → 120 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT135 °C65 °C49.26 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 135 to 65 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 135 → 65 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 144 kW
  2. 2. ΔTlm = 59.44 K
  3. 3. U = 916.5 W/(m²·K)
  4. 4. A = 2.572 m²
  5. 5. A = 3.869 m²
  6. 6. A = 1.777 m²

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