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
lengthT120 °C85 °C15 °C25 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 120 to 85 °C while the cold fluid heats from 15 to 25 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 85 °CTc: 15 → 25 °C
ΔTlm = K
2.Easy
lengthT170 °C135 °C150 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 170 to 135 °C while the cold fluid heats from 30 to 150 °C. Find the log-mean temperature difference ΔTlm.

Th: 170 → 135 °CTc: 30 → 150 °C
ΔTlm = K
3.Medium
lengthT100 °C20 °C50 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 50 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 50 °CU = 1000 W/(m²·K)
A = m²
4.Medium
lengthT175 °C135 °C20 °C100 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 40 kW. The hot fluid cools from 175 to 135 °C and the cold fluid heats from 20 to 100 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 40 kWU = 800 W/(m²·K)Th: 175 → 135 °CTc: 20 → 100 °C
A = m²
5.Hard
lengthT125 °C??15 °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 125 °C and the cold stream at 15 °C. The exchanger has A = 4 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 125 °CTc,in = 15 °CA = 4 m²U = 200 W/(m²·K)
Th,out = °C
6.Hard
lengthT110 °C70 °C98.04 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 110 to 70 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 110 → 70 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 80.41 K
  2. 2. ΔTlm = 51.26 K
  3. 3. A = 5.894 m²
  4. 4. A = 0.62 m²
  5. 5. Th,out = 57.31 °C
  6. 6. A = 4.118 m²

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