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
lengthT85 °C50 °C60 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1.5 m² and an overall heat transfer coefficient of 200 W/(m²·K). The hot fluid cools from 85 to 50 °C and the cold fluid heats from 20 to 60 °C. Find the heat transfer rate Q̇.

A = 1.5 m²U = 200 W/(m²·K)Th: 85 → 50 °CTc: 20 → 60 °C
Q̇ = kW
2.Easy
lengthT130 °C55 °C?15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 130 to 55 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 130 → 55 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
3.Medium
lengthT180 °C65 °C140 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 310 kW. The hot fluid cools from 180 to 65 °C and the cold fluid heats from 30 to 140 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 310 kWU = 1500 W/(m²·K)Th: 180 → 65 °CTc: 30 → 140 °C
A = m²
4.Medium
lengthT165 °C75 °C50 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 190 kW. The hot fluid cools from 165 to 75 °C and the cold fluid heats from 30 to 50 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 190 kWU = 1000 W/(m²·K)Th: 165 → 75 °CTc: 30 → 50 °C
A = m²
5.Hard
lengthT90 °C55 °C23.79 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 90 to 55 °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 = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 90 → 55 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT80 °C45 °C27.93 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 80 to 45 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 80 → 45 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 8.227 kW
  2. 2. Tc,out = 33.84 °C
  3. 3. A = 5.519 m²
  4. 4. A = 2.547 m²
  5. 5. A = 2.12 m²
  6. 6. A = 1.096 m²

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