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 °C40 °C110 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 10 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 125 to 40 °C and the cold fluid heats from 20 to 110 °C. Find the heat transfer rate Q̇.

A = 10 m²U = 800 W/(m²·K)Th: 125 → 40 °CTc: 20 → 110 °C
Q̇ = kW
2.Easy
lengthT90 °C45 °C55 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 90 to 45 °C and the cold fluid heats from 25 to 55 °C. Find the heat transfer rate Q̇.

A = 1 m²U = 1500 W/(m²·K)Th: 90 → 45 °CTc: 25 → 55 °C
Q̇ = kW
3.Medium
lengthT120 °C10 °C55 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °C on the outside of the tubes. Cooling water (5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 55 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 55 °CU = 1000 W/(m²·K)
A = m²
4.Medium
lengthT80 °C50 °C55 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 390 kW. The hot fluid cools from 80 to 50 °C and the cold fluid heats from 30 to 55 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWU = 200 W/(m²·K)Th: 80 → 50 °CTc: 30 → 55 °C
A = m²
5.Hard
lengthT85 °C??15 °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 85 °C and the cold stream at 15 °C. The exchanger has A = 1 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 85 °CTc,in = 15 °CA = 1 m²U = 300 W/(m²·K)
Th,out = °C
6.Hard
lengthT150 °C120 °C42.01 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 150 to 120 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °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: 150 → 120 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 139 kW
  2. 2. Q̇ = 40.21 kW
  3. 3. A = 11 m²
  4. 4. A = 87.03 m²
  5. 5. Th,out = 68.85 °C
  6. 6. A = 0.8851 m²

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