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 0.8 kg/s of ethanol (cp = 2.44 kJ/(kg·K)) is heated from 30 to 75 °C. Find the heat transfer rate Q̇.

ṁ = 0.8 kg/scp = 2.44 kJ/(kg·K)T: 30 → 75 °C
Q̇ = kW
2.Easy
lengthT165 °C110 °C?10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 165 to 110 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 165 → 110 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
3.Medium
lengthT100 °C30 °C90 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °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 30 to 90 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 30 → 90 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT135 °C65 °C110 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 20 kW. The hot fluid cools from 135 to 65 °C and the cold fluid heats from 15 to 110 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 20 kWU = 800 W/(m²·K)Th: 135 → 65 °CTc: 15 → 110 °C
A = m²
5.Hard
lengthT120 °C75 °C21.3 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 120 to 75 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 120 → 75 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT180 °C70 °C151.6 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 180 to 70 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 180 → 70 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 87.84 kW
  2. 2. Tc,out = 42.89 °C
  3. 3. A = 2.324 m²
  4. 4. A = 0.6931 m²
  5. 5. A = 1.464 m²
  6. 6. A = 35.99 m²

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