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
lengthT165 °C130 °C80 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1.5 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 165 to 130 °C and the cold fluid heats from 15 to 80 °C. Find the heat transfer rate Q̇.

A = 1.5 m²U = 800 W/(m²·K)Th: 165 → 130 °CTc: 15 → 80 °C
Q̇ = kW
2.Easy
lengthT175 °C40 °C150 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 4 m² and an overall heat transfer coefficient of 1000 W/(m²·K). The hot fluid cools from 175 to 40 °C and the cold fluid heats from 25 to 150 °C. Find the heat transfer rate Q̇.

A = 4 m²U = 1000 W/(m²·K)Th: 175 → 40 °CTc: 25 → 150 °C
Q̇ = kW
3.Medium
lengthT110 °C65 °C60 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 390 kW. The hot fluid cools from 110 to 65 °C and the cold fluid heats from 30 to 60 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWU = 800 W/(m²·K)Th: 110 → 65 °CTc: 30 → 60 °C
A = m²
4.Medium
lengthT100 °C25 °C80 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 25 to 80 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 80 °CU = 1500 W/(m²·K)
A = m²
5.Hard
lengthT100 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 100 °C on the outside of the tubes of a condenser with a heat transfer area of 1.5 m² and U = 3000 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 1.5 m²U = 3000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT120 °C80 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 120 to 80 °C. Water (0.3 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 40 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 120 → 80 °Cṁc = 0.3 kg/sTc,in = 15 °CD = 40 mmU = 500 W/(m²·K)
L = m

Answer key

  1. 1. Q̇ = 119.1 kW
  2. 2. Q̇ = 78.3 kW
  3. 3. A = 11.59 m²
  4. 4. A = 7.367 m²
  5. 5. Tc,out = 60.97 °C
  6. 6. L = 5.383 m

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