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
lengthT160 °C120 °C120 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 120 °C while the cold fluid heats from 15 to 120 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 120 °CTc: 15 → 120 °C
ΔTlm = K
2.Easy

In a heat exchanger 3 kg/s of water (cp = 4.18 kJ/(kg·K)) is heated from 30 to 80 °C. Find the heat transfer rate Q̇.

ṁ = 3 kg/scp = 4.18 kJ/(kg·K)T: 30 → 80 °C
Q̇ = kW
3.Medium
lengthT100 °C15 °C70 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 15 to 70 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc: 15 → 70 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT80 °C55 °C25 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 320 kW. The hot fluid cools from 80 to 55 °C and the cold fluid heats from 25 to 50 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 320 kWU = 300 W/(m²·K)Th: 80 → 55 °CTc: 25 → 50 °C
A = m²
5.Hard
lengthT135 °C75 °C41.91 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 135 to 75 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 135 → 75 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT175 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 0.5 kW/K. The hot stream enters at 175 °C and the cold stream at 25 °C. The exchanger has A = 3 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 175 °CTc,in = 25 °CA = 3 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 67.35 K
  2. 2. Q̇ = 627 kW
  3. 3. A = 1.866 m²
  4. 4. A = 51.16 m²
  5. 5. A = 9.955 m²
  6. 6. Th,out = 93.18 °C

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