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 0.3 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is heated from 25 to 85 °C. Find the heat transfer rate Q̇.

ṁ = 0.3 kg/scp = 2.1 kJ/(kg·K)T: 25 → 85 °C
Q̇ = kW
2.Easy
lengthT125 °C90 °C95 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 125 to 90 °C while the cold fluid heats from 25 to 95 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 90 °CTc: 25 → 95 °C
ΔTlm = K
3.Medium
lengthT120 °C15 °C100 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °C on the outside of the tubes. Cooling water (4 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 15 to 100 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 4 kg/scp = 4.18 kJ/(kg·K)Tc: 15 → 100 °CU = 2000 W/(m²·K)
A = m²
4.Medium
lengthT150 °C135 °C125 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 70 kW. Its heat transfer area is 4 m². The hot fluid cools from 150 to 135 °C and the cold fluid heats from 30 to 125 °C. Find the overall heat transfer coefficient U.

Q̇ = 70 kWA = 4 m²Th: 150 → 135 °CTc: 30 → 125 °C
U = W/(m²·K)
5.Hard
lengthT130 °C95 °C68.52 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 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 30 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 130 → 95 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT85 °C??30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 85 °C and the cold stream at 30 °C. The exchanger has A = 3 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 85 °CTc,in = 30 °CA = 3 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 37.8 kW
  2. 2. ΔTlm = 45.27 K
  3. 3. A = 13.86 m²
  4. 4. U = 313.9 W/(m²·K)
  5. 5. A = 3.183 m²
  6. 6. Th,out = 61.43 °C

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