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 1.2 kg/s of water (cp = 4.18 kJ/(kg·K)) is heated from 40 to 70 °C. Find the heat transfer rate Q̇.

ṁ = 1.2 kg/scp = 4.18 kJ/(kg·K)T: 40 → 70 °C
Q̇ = kW
2.Easy
lengthT130 °C85 °C115 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 85 °C while the cold fluid heats from 30 to 115 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 85 °CTc: 30 → 115 °C
ΔTlm = K
3.Medium
lengthT130 °C15 °C30 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °C on the outside of the tubes. Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 15 to 30 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc: 15 → 30 °CU = 1500 W/(m²·K)
A = m²
4.Medium
lengthT130 °C15 °C95 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °C on the outside of the tubes. Cooling water (4 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 15 to 95 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 4 kg/scp = 4.18 kJ/(kg·K)Tc: 15 → 95 °CU = 3000 W/(m²·K)
A = m²
5.Hard
lengthT120 °C50 °C56.87 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 50 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 50 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT180 °C??10 °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 180 °C and the cold stream at 10 °C. The exchanger has A = 3 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 180 °CTc,in = 10 °CA = 3 m²U = 800 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 150.5 kW
  2. 2. ΔTlm = 30.79 K
  3. 3. A = 0.5842 m²
  4. 4. A = 6.63 m²
  5. 5. A = 5.504 m²
  6. 6. Th,out = 75.38 °C

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