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
lengthT145 °C90 °C90 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 145 to 90 °C while the cold fluid heats from 10 to 90 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 90 °CTc: 10 → 90 °C
ΔTlm = K
2.Easy
lengthT145 °C55 °C80 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 3 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 145 to 55 °C and the cold fluid heats from 10 to 80 °C. Find the heat transfer rate Q̇.

A = 3 m²U = 500 W/(m²·K)Th: 145 → 55 °CTc: 10 → 80 °C
Q̇ = kW
3.Medium
lengthT140 °C10 °C65 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 65 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 65 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT155 °C60 °C45 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 40 kW. The hot fluid cools from 155 to 60 °C and the cold fluid heats from 10 to 45 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 40 kWU = 300 W/(m²·K)Th: 155 → 60 °CTc: 10 → 45 °C
A = m²
5.Hard
lengthT130 °C??10 °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 130 °C and the cold stream at 10 °C. The exchanger has A = 1 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 130 °CTc,in = 10 °CA = 1 m²U = 300 W/(m²·K)
Th,out = °C
6.Hard
lengthT145 °C75 °C48.44 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 145 to 75 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 145 → 75 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 66.72 K
  2. 2. Q̇ = 81.58 kW
  3. 3. A = 0.6569 m²
  4. 4. A = 1.752 m²
  5. 5. Th,out = 85 °C
  6. 6. A = 4.156 m²

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