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
lengthT145 °C100 °C50 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 145 to 100 °C while the cold fluid heats from 30 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 100 °CTc: 30 → 50 °C
ΔTlm = K
2.Easy
lengthT150 °C110 °C70 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 150 to 110 °C while the cold fluid heats from 20 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 110 °CTc: 20 → 70 °C
ΔTlm = K
3.Medium
lengthT100 °C30 °C50 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 30 to 50 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 30 → 50 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT120 °C10 °C40 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °C on the outside of the tubes. Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 40 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 40 °CU = 3500 W/(m²·K)
A = m²
5.Hard
lengthT110 °C55 °C34.61 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 110 to 55 °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 = 2.1 kJ/(kg·K)Th: 110 → 55 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT105 °C30 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 105 °C on the outside of the tubes of a condenser with a heat transfer area of 3 m² and U = 3000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 3 m²U = 3000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 81.86 K
  2. 2. ΔTlm = 84.9 K
  3. 3. A = 2.009 m²
  4. 4. A = 1.141 m²
  5. 5. A = 6.325 m²
  6. 6. Tc,out = 68.41 °C

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