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
lengthT130 °C85 °C10 °C70 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 130 to 85 °C while the cold fluid heats from 10 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 85 °CTc: 10 → 70 °C
ΔTlm = K
2.Easy
lengthT130 °C35 °C90 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 20 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 130 to 35 °C and the cold fluid heats from 20 to 90 °C. Find the heat transfer rate Q̇.

A = 20 m²U = 500 W/(m²·K)Th: 130 → 35 °CTc: 20 → 90 °C
Q̇ = kW
3.Medium
lengthT120 °C25 °C70 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °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 25 to 70 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 70 °CU = 3000 W/(m²·K)
A = m²
4.Medium
lengthT120 °C20 °C35 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °C on the outside of the tubes. Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 35 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 35 °CU = 3500 W/(m²·K)
A = m²
5.Hard
lengthT140 °C95 °C25 °C?ΔT₁ΔT₂parallel flow

In a parallel-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 140 to 95 °C. Water (1 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 25 °C. The inner tube has a diameter of 20 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: 140 → 95 °Cṁc = 1 kg/sTc,in = 25 °CD = 20 mmU = 500 W/(m²·K)
L = m
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 2.5 m² and U = 3000 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 2.5 m²U = 3000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 50.49 K
  2. 2. Q̇ = 254.9 kW
  3. 3. A = 1.789 m²
  4. 4. A = 0.09705 m²
  5. 5. L = 33.72 m
  6. 6. Tc,out = 92.53 °C

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