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 °C130 °C120 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 12 m² and an overall heat transfer coefficient of 200 W/(m²·K). The hot fluid cools from 145 to 130 °C and the cold fluid heats from 25 to 120 °C. Find the heat transfer rate Q̇.

A = 12 m²U = 200 W/(m²·K)Th: 145 → 130 °CTc: 25 → 120 °C
Q̇ = kW
2.Easy
lengthT135 °C80 °C105 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 80 °C while the cold fluid heats from 15 to 105 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 80 °CTc: 15 → 105 °C
ΔTlm = K
3.Medium
lengthT125 °C85 °C65 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 270 kW. The hot fluid cools from 125 to 85 °C and the cold fluid heats from 30 to 65 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 270 kWU = 1000 W/(m²·K)Th: 125 → 85 °CTc: 30 → 65 °C
A = m²
4.Medium
lengthT140 °C30 °C85 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °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 30 to 85 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc: 30 → 85 °CU = 1500 W/(m²·K)
A = m²
5.Hard
lengthT175 °C??30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 175 °C and the cold stream at 30 °C. The exchanger has A = 5 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 175 °CTc,in = 30 °CA = 5 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT80 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 80 °C and the cold stream at 25 °C. The exchanger has A = 5 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 80 °CTc,in = 25 °CA = 5 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 133.8 kW
  2. 2. ΔTlm = 45.27 K
  3. 3. A = 4.699 m²
  4. 4. A = 2.897 m²
  5. 5. Th,out = 69.55 °C
  6. 6. Th,out = 58 °C

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