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 water (cp = 4.18 kJ/(kg·K)) is cooled from 75 to 60 °C. Find the heat transfer rate Q̇.

ṁ = 2.5 kg/scp = 4.18 kJ/(kg·K)T: 75 → 60 °C
Q̇ = kW
2.Easy
lengthT100 °C65 °C60 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 100 to 65 °C while the cold fluid heats from 15 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 100 → 65 °CTc: 15 → 60 °C
ΔTlm = K
3.Medium
lengthT135 °C45 °C120 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 480 kW. The hot fluid cools from 135 to 45 °C and the cold fluid heats from 25 to 120 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 480 kWU = 200 W/(m²·K)Th: 135 → 45 °CTc: 25 → 120 °C
A = m²
4.Medium
lengthT160 °C140 °C45 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 70 kW. The hot fluid cools from 160 to 140 °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 = 70 kWU = 200 W/(m²·K)Th: 160 → 140 °CTc: 15 → 45 °C
A = m²
5.Hard
lengthT90 °C60 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.8 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 90 to 60 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °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 = 0.8 kg/scp,h = 2.3 kJ/(kg·K)Th: 90 → 60 °Cṁc = 0.5 kg/sTc,in = 10 °CD = 40 mmU = 500 W/(m²·K)
L = m
6.Hard
lengthT140 °C20 °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 3 m² and U = 2000 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 = 140 °CA = 3 m²U = 2000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C

Answer key

  1. 1. Q̇ = 156.8 kW
  2. 2. ΔTlm = 44.81 K
  3. 3. A = 138.1 m²
  4. 4. A = 2.918 m²
  5. 5. L = 16.97 m
  6. 6. Tc,out = 93.91 °C

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