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
lengthT160 °C75 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 160 to 75 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 160 → 75 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
2.Easy

In a heat exchanger 3 kg/s of water (cp = 4.18 kJ/(kg·K)) is heated from 40 to 65 °C. Find the heat transfer rate Q̇.

ṁ = 3 kg/scp = 4.18 kJ/(kg·K)T: 40 → 65 °C
Q̇ = kW
3.Medium
lengthT120 °C85 °C85 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 650 kW. The hot fluid cools from 120 to 85 °C and the cold fluid heats from 15 to 85 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 650 kWF = 0.9U = 500 W/(m²·K)Th: 120 → 85 °CTc: 15 → 85 °C
A = m²
4.Medium
lengthT175 °C60 °C15 °C55 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 140 kW. The hot fluid cools from 175 to 60 °C and the cold fluid heats from 15 to 55 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 140 kWU = 1000 W/(m²·K)Th: 175 → 60 °CTc: 15 → 55 °C
A = m²
5.Hard
lengthT120 °C65 °C45.18 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 120 to 65 °C in a counter-flow exchanger. It heats 3 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 = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 120 → 65 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT175 °C??30 °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 175 °C and the cold stream at 30 °C. The exchanger has A = 5 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 4 kW/KTh,in = 175 °CTc,in = 30 °CA = 5 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Tc,out = 92.36 °C
  2. 2. Q̇ = 313.5 kW
  3. 3. A = 28.61 m²
  4. 4. A = 3.13 m²
  5. 5. A = 9.1 m²
  6. 6. Th,out = 119.2 °C

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