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

In a heat exchanger 1 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is cooled from 60 to 35 °C. Find the heat transfer rate Q̇.

ṁ = 1 kg/scp = 2.1 kJ/(kg·K)T: 60 → 35 °C
Q̇ = kW
2.Easy
lengthT115 °C65 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 115 to 65 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 115 → 65 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
3.Medium
lengthT115 °C55 °C60 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 480 kW. The hot fluid cools from 115 to 55 °C and the cold fluid heats from 30 to 60 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 480 kWU = 300 W/(m²·K)Th: 115 → 55 °CTc: 30 → 60 °C
A = m²
4.Medium
lengthT90 °C35 °C45 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 300 kW. The hot fluid cools from 90 to 35 °C and the cold fluid heats from 15 to 45 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 200 W/(m²·K)Th: 90 → 35 °CTc: 15 → 45 °C
A = m²
5.Hard
lengthT140 °C15 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 140 °C on the outside of the tubes of a condenser with a heat transfer area of 2 m² and U = 2000 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 2 m²U = 2000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
6.Hard
lengthT105 °C??30 °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 105 °C and the cold stream at 30 °C. The exchanger has A = 0.5 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 105 °CTc,in = 30 °CA = 0.5 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 52.5 kW
  2. 2. Tc,out = 67.68 °C
  3. 3. A = 42.05 m²
  4. 4. A = 48.66 m²
  5. 5. Tc,out = 91.99 °C
  6. 6. Th,out = 80 °C

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