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 2.5 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is cooled from 120 to 75 °C. Find the heat transfer rate Q̇.

ṁ = 2.5 kg/scp = 2.1 kJ/(kg·K)T: 120 → 75 °C
Q̇ = kW
2.Easy
lengthT85 °C55 °C40 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 55 °C while the cold fluid heats from 30 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 55 °CTc: 30 → 40 °C
ΔTlm = K
3.Medium
lengthT130 °C85 °C85 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 300 kW. The hot fluid cools from 130 to 85 °C and the cold fluid heats from 10 to 85 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 800 W/(m²·K)Th: 130 → 85 °CTc: 10 → 85 °C
A = m²
4.Medium
lengthT150 °C65 °C20 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 180 kW. The hot fluid cools from 150 to 65 °C and the cold fluid heats from 20 to 60 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 180 kWU = 1500 W/(m²·K)Th: 150 → 65 °CTc: 20 → 60 °C
A = m²
5.Hard
lengthT130 °C105 °C42.51 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 130 to 105 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 130 → 105 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT100 °C15 °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 5 m² and U = 2000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 5 m²U = 2000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C

Answer key

  1. 1. Q̇ = 236.3 kW
  2. 2. ΔTlm = 34.03 K
  3. 3. A = 6.385 m²
  4. 4. A = 3.128 m²
  5. 5. A = 0.81 m²
  6. 6. Tc,out = 61.71 °C

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