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 °C75 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 115 to 75 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 115 → 75 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
2.Easy
lengthT170 °C85 °C30 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 170 to 85 °C while the cold fluid heats from 15 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 170 → 85 °CTc: 15 → 30 °C
ΔTlm = K
3.Medium
lengthT135 °C115 °C25 °C75 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 290 kW. The hot fluid cools from 135 to 115 °C and the cold fluid heats from 25 to 75 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 290 kWU = 500 W/(m²·K)Th: 135 → 115 °CTc: 25 → 75 °C
A = m²
4.Medium
lengthT105 °C10 °C85 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 105 °C on the outside of the tubes. Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 85 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 105 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 85 °CU = 3000 W/(m²·K)
A = m²
5.Hard
lengthT125 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 125 °C and the cold stream at 25 °C. The exchanger has A = 1 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 125 °CTc,in = 25 °CA = 1 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT95 °C??20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 4 kW/K. The hot stream enters at 95 °C and the cold stream at 20 °C. The exchanger has A = 6 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 4 kW/KTh,in = 95 °CTc,in = 20 °CA = 6 m²U = 300 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Tc,out = 69.02 °C
  2. 2. ΔTlm = 101 K
  3. 3. A = 8.382 m²
  4. 4. A = 2.171 m²
  5. 5. Th,out = 90.22 °C
  6. 6. Th,out = 71.72 °C

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