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
lengthT140 °C55 °C35 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 140 to 55 °C while the cold fluid heats from 15 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 55 °CTc: 15 → 35 °C
ΔTlm = K
2.Easy
lengthT130 °C75 °C?10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 130 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. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 130 → 75 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
3.Medium
lengthT100 °C10 °C75 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (4 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 75 °C. The overall heat transfer coefficient is 2500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 4 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 75 °CU = 2500 W/(m²·K)
A = m²
4.Medium
lengthT110 °C75 °C65 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 320 kW. The hot fluid cools from 110 to 75 °C and the cold fluid heats from 25 to 65 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 320 kWU = 200 W/(m²·K)Th: 110 → 75 °CTc: 25 → 65 °C
A = m²
5.Hard
lengthT140 °C60 °C62.85 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 140 to 60 °C in a counter-flow exchanger. It heats 1.5 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 = 2.5 kJ/(kg·K)Th: 140 → 60 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT145 °C125 °C32.34 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 145 to 125 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 145 → 125 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 67.35 K
  2. 2. Tc,out = 37.63 °C
  3. 3. A = 8.567 m²
  4. 4. A = 33.72 m²
  5. 5. A = 16.77 m²
  6. 6. A = 0.5414 m²

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