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
lengthT110 °C80 °C20 °C30 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 110 to 80 °C while the cold fluid heats from 20 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 80 °CTc: 20 → 30 °C
ΔTlm = K
2.Easy
lengthT130 °C95 °C?20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 130 to 95 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 130 → 95 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
3.Medium
lengthT110 °C25 °C10 °C20 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 190 kW. The hot fluid cools from 110 to 25 °C and the cold fluid heats from 10 to 20 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 190 kWU = 1500 W/(m²·K)Th: 110 → 25 °CTc: 10 → 20 °C
A = m²
4.Medium
lengthT130 °C80 °C20 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 160 kW. The hot fluid cools from 130 to 80 °C and the cold fluid heats from 20 to 60 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 160 kWU = 1000 W/(m²·K)Th: 130 → 80 °CTc: 20 → 60 °C
A = m²
5.Hard
lengthT155 °C75 °C25 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 155 to 75 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 25 °C. The inner tube has a diameter of 25 mm, and U = 400 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 75 °Cṁc = 1.5 kg/sTc,in = 25 °CD = 25 mmU = 400 W/(m²·K)
L = m
6.Hard
lengthT100 °C20 °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 1.5 m² and U = 2500 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 1.5 m²U = 2500 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 68.05 K
  2. 2. Tc,out = 61.87 °C
  3. 3. A = 3.994 m²
  4. 4. A = 3.031 m²
  5. 5. L = 20.61 m
  6. 6. Tc,out = 48.92 °C

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