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
lengthT115 °C90 °C75 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 90 °C while the cold fluid heats from 25 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 90 °CTc: 25 → 75 °C
ΔTlm = K
2.Easy
lengthT80 °C55 °C60 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 80 to 55 °C while the cold fluid heats from 20 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 80 → 55 °CTc: 20 → 60 °C
ΔTlm = K
3.Medium
lengthT175 °C50 °C95 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 330 kW. The hot fluid cools from 175 to 50 °C and the cold fluid heats from 30 to 95 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 330 kWU = 800 W/(m²·K)Th: 175 → 50 °CTc: 30 → 95 °C
A = m²
4.Medium
lengthT180 °C140 °C30 °C120 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 40 kW. The hot fluid cools from 180 to 140 °C and the cold fluid heats from 30 to 120 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 40 kWU = 1000 W/(m²·K)Th: 180 → 140 °CTc: 30 → 120 °C
A = m²
5.Hard
lengthT120 °C95 °C59.86 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 95 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 95 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT105 °C25 °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 5 m² and U = 1000 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 = 105 °CA = 5 m²U = 1000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 51.49 K
  2. 2. ΔTlm = 26.8 K
  3. 3. A = 9.531 m²
  4. 4. A = 0.62 m²
  5. 5. A = 2.694 m²
  6. 6. Tc,out = 51.31 °C

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