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
lengthT115 °C65 °C85 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 65 °C while the cold fluid heats from 25 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 65 °CTc: 25 → 85 °C
ΔTlm = K
2.Easy
lengthT130 °C70 °C110 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 3 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 130 to 70 °C and the cold fluid heats from 25 to 110 °C. Find the heat transfer rate Q̇.

A = 3 m²U = 800 W/(m²·K)Th: 130 → 70 °CTc: 25 → 110 °C
Q̇ = kW
3.Medium
lengthT180 °C160 °C65 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 290 kW. The hot fluid cools from 180 to 160 °C and the cold fluid heats from 20 to 65 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 290 kWU = 500 W/(m²·K)Th: 180 → 160 °CTc: 20 → 65 °C
A = m²
4.Medium
lengthT120 °C20 °C55 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °C on the outside of the tubes. Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 55 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 55 °CU = 3000 W/(m²·K)
A = m²
5.Hard
lengthT145 °C125 °C31.99 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 145 to 125 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 145 → 125 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT145 °C60 °C108.5 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 145 to 60 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 145 → 60 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 34.76 K
  2. 2. Q̇ = 73.99 kW
  3. 3. A = 4.564 m²
  4. 4. A = 0.6002 m²
  5. 5. A = 1.205 m²
  6. 6. A = 9.635 m²

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