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
lengthT115 °C95 °C80 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 115 to 95 °C and the cold fluid heats from 10 to 80 °C. Find the heat transfer rate Q̇.

A = 1 m²U = 500 W/(m²·K)Th: 115 → 95 °CTc: 10 → 80 °C
Q̇ = kW
2.Easy
lengthT125 °C90 °C60 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 125 to 90 °C while the cold fluid heats from 20 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 90 °CTc: 20 → 60 °C
ΔTlm = K
3.Medium
lengthT125 °C85 °C50 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 230 kW. The hot fluid cools from 125 to 85 °C and the cold fluid heats from 30 to 50 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 230 kWU = 1000 W/(m²·K)Th: 125 → 85 °CTc: 30 → 50 °C
A = m²
4.Medium
lengthT150 °C100 °C90 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 390 kW. The hot fluid cools from 150 to 100 °C and the cold fluid heats from 15 to 90 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWU = 1000 W/(m²·K)Th: 150 → 100 °CTc: 15 → 90 °C
A = m²
5.Hard
lengthT175 °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 175 °C and the cold stream at 30 °C. The exchanger has A = 6 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 175 °CTc,in = 30 °CA = 6 m²U = 200 W/(m²·K)
Th,out = °C
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 2 m² and U = 2500 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 2 m²U = 2500 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C

Answer key

  1. 1. Q̇ = 28.18 kW
  2. 2. ΔTlm = 67.47 K
  3. 3. A = 3.567 m²
  4. 4. A = 5.434 m²
  5. 5. Th,out = 72.65 °C
  6. 6. Tc,out = 53.26 °C

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