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 water (cp = 4.18 kJ/(kg·K)) is cooled from 75 to 35 °C. Find the heat transfer rate Q̇.

ṁ = 1 kg/scp = 4.18 kJ/(kg·K)T: 75 → 35 °C
Q̇ = kW
2.Easy
lengthT90 °C45 °C15 °C25 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 45 °C while the cold fluid heats from 15 to 25 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 45 °CTc: 15 → 25 °C
ΔTlm = K
3.Medium
lengthT145 °C100 °C110 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 370 kW. The hot fluid cools from 145 to 100 °C and the cold fluid heats from 15 to 110 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 370 kWU = 500 W/(m²·K)Th: 145 → 100 °CTc: 15 → 110 °C
A = m²
4.Medium
lengthT175 °C50 °C35 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 280 kW. Its heat transfer area is 2 m². The hot fluid cools from 175 to 50 °C and the cold fluid heats from 20 to 35 °C. Find the overall heat transfer coefficient U.

Q̇ = 280 kWA = 2 m²Th: 175 → 50 °CTc: 20 → 35 °C
U = W/(m²·K)
5.Hard
lengthT140 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 140 °C and the cold stream at 10 °C. The exchanger has A = 3 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 140 °CTc,in = 10 °CA = 3 m²U = 200 W/(m²·K)
Th,out = °C
6.Hard
lengthT130 °C15 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 1.5 m² and U = 2500 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 = 130 °CA = 1.5 m²U = 2500 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C

Answer key

  1. 1. Q̇ = 167.2 kW
  2. 2. ΔTlm = 41.61 K
  3. 3. A = 13.13 m²
  4. 4. U = 1961 W/(m²·K)
  5. 5. Th,out = 110 °C
  6. 6. Tc,out = 83.11 °C

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