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
lengthT165 °C135 °C?15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 165 to 135 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °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: 165 → 135 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
2.Easy

In a heat exchanger 3 kg/s of ethanol (cp = 2.44 kJ/(kg·K)) is cooled from 65 to 35 °C. Find the heat transfer rate Q̇.

ṁ = 3 kg/scp = 2.44 kJ/(kg·K)T: 65 → 35 °C
Q̇ = kW
3.Medium
lengthT130 °C25 °C110 °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 25 to 110 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 4 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 110 °CU = 1500 W/(m²·K)
A = m²
4.Medium
lengthT155 °C30 °C105 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 690 kW. The hot fluid cools from 155 to 30 °C and the cold fluid heats from 10 to 105 °C. The LMTD correction factor for this arrangement is F = 0.85, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 690 kWF = 0.85U = 1000 W/(m²·K)Th: 155 → 30 °CTc: 10 → 105 °C
A = m²
5.Hard
lengthT165 °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 165 °C and the cold stream at 30 °C. The exchanger has A = 4 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 165 °CTc,in = 30 °CA = 4 m²U = 300 W/(m²·K)
Th,out = °C
6.Hard
lengthT175 °C80 °C81.82 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 175 to 80 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 175 → 80 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 23.25 °C
  2. 2. Q̇ = 219.6 kW
  3. 3. A = 18.48 m²
  4. 4. A = 24.79 m²
  5. 5. Th,out = 69.71 °C
  6. 6. A = 6.559 m²

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