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
lengthT165 °C50 °C45 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 165 to 50 °C while the cold fluid heats from 10 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 165 → 50 °CTc: 10 → 45 °C
ΔTlm = K
2.Easy
lengthT115 °C75 °C?10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 115 to 75 °C in a counter-flow exchanger. It heats 1.5 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 = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 115 → 75 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
3.Medium
lengthT180 °C70 °C115 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 90 kW. The hot fluid cools from 180 to 70 °C and the cold fluid heats from 25 to 115 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 90 kWU = 200 W/(m²·K)Th: 180 → 70 °CTc: 25 → 115 °C
A = m²
4.Medium
lengthT140 °C15 °C55 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 15 to 55 °C. The overall heat transfer coefficient is 2500 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc: 15 → 55 °CU = 2500 W/(m²·K)
A = m²
5.Hard
lengthT155 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 155 °C and the cold stream at 10 °C. The exchanger has A = 0.5 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 155 °CTc,in = 10 °CA = 0.5 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT105 °C75 °C37.94 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 105 to 75 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 105 → 75 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 72.82 K
  2. 2. Tc,out = 17.34 °C
  3. 3. A = 8.274 m²
  4. 4. A = 1.29 m²
  5. 5. Th,out = 113.6 °C
  6. 6. A = 2.466 m²

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