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

In a heat exchanger 0.8 kg/s of ethanol (cp = 2.44 kJ/(kg·K)) is heated from 15 to 85 °C. Find the heat transfer rate Q̇.

ṁ = 0.8 kg/scp = 2.44 kJ/(kg·K)T: 15 → 85 °C
Q̇ = kW
2.Easy
lengthT130 °C90 °C100 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 90 °C while the cold fluid heats from 25 to 100 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 90 °CTc: 25 → 100 °C
ΔTlm = K
3.Medium
lengthT140 °C110 °C65 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 490 kW. The hot fluid cools from 140 to 110 °C and the cold fluid heats from 15 to 65 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 490 kWU = 300 W/(m²·K)Th: 140 → 110 °CTc: 15 → 65 °C
A = m²
4.Medium
lengthT125 °C50 °C10 °C35 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 360 kW. Its heat transfer area is 2 m². The hot fluid cools from 125 to 50 °C and the cold fluid heats from 10 to 35 °C. Find the overall heat transfer coefficient U.

Q̇ = 360 kWA = 2 m²Th: 125 → 50 °CTc: 10 → 35 °C
U = W/(m²·K)
5.Hard
lengthT100 °C30 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 100 °C on the outside of the tubes of a condenser with a heat transfer area of 2 m² and U = 2500 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 2 m²U = 2500 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
6.Hard
lengthT145 °C90 °C?25 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 145 to 90 °C. Water (0.3 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 = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 145 → 90 °Cṁc = 0.3 kg/sTc,in = 25 °CD = 20 mmU = 250 W/(m²·K)
L = m

Answer key

  1. 1. Q̇ = 136.6 kW
  2. 2. ΔTlm = 45.27 K
  3. 3. A = 19.31 m²
  4. 4. U = 3666 W/(m²·K)
  5. 5. Tc,out = 68.47 °C
  6. 6. L = 214.8 m

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