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
lengthT125 °C95 °C25 °C90 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 125 to 95 °C while the cold fluid heats from 25 to 90 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 95 °CTc: 25 → 90 °C
ΔTlm = K
2.Easy
lengthT160 °C145 °C70 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 145 °C while the cold fluid heats from 30 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 145 °CTc: 30 → 70 °C
ΔTlm = K
3.Medium
lengthT140 °C20 °C85 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °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 20 to 85 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 85 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT140 °C30 °C75 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °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 30 to 75 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 4 kg/scp = 4.18 kJ/(kg·K)Tc: 30 → 75 °CU = 1500 W/(m²·K)
A = m²
5.Hard
lengthT120 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 120 °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 25 °C. Find the water outlet temperature Tc,out.

Ts = 120 °CA = 3 m²U = 3000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT100 °C60 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.8 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 100 to 60 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 32 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.8 kg/scp,h = 2.3 kJ/(kg·K)Th: 100 → 60 °Cṁc = 0.5 kg/sTc,in = 15 °CD = 32 mmU = 500 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 31.71 K
  2. 2. ΔTlm = 102 K
  3. 3. A = 2.795 m²
  4. 4. A = 5.864 m²
  5. 5. Tc,out = 73.65 °C
  6. 6. L = 30.92 m

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