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
lengthT125 °C45 °C75 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 125 to 45 °C while the cold fluid heats from 20 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 45 °CTc: 20 → 75 °C
ΔTlm = K
2.Easy
lengthT175 °C90 °C120 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 90 °C while the cold fluid heats from 20 to 120 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 90 °CTc: 20 → 120 °C
ΔTlm = K
3.Medium
lengthT155 °C120 °C45 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 220 kW. Its heat transfer area is 3 m². The hot fluid cools from 155 to 120 °C and the cold fluid heats from 30 to 45 °C. Find the overall heat transfer coefficient U.

Q̇ = 220 kWA = 3 m²Th: 155 → 120 °CTc: 30 → 45 °C
U = W/(m²·K)
4.Medium
lengthT100 °C25 °C75 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °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 25 to 75 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 75 °CU = 2000 W/(m²·K)
A = m²
5.Hard
lengthT150 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 150 °C and the cold stream at 25 °C. The exchanger has A = 1 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 150 °CTc,in = 25 °CA = 1 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT90 °C??25 °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 90 °C and the cold stream at 25 °C. The exchanger has A = 4 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 90 °CTc,in = 25 °CA = 4 m²U = 300 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 36.07 K
  2. 2. ΔTlm = 62.2 K
  3. 3. U = 735.8 W/(m²·K)
  4. 4. A = 2.296 m²
  5. 5. Th,out = 94.44 °C
  6. 6. Th,out = 65.63 °C

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