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
lengthT170 °C95 °C115 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1.5 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 170 to 95 °C and the cold fluid heats from 10 to 115 °C. Find the heat transfer rate Q̇.

A = 1.5 m²U = 1500 W/(m²·K)Th: 170 → 95 °CTc: 10 → 115 °C
Q̇ = kW
2.Easy

In a heat exchanger 3 kg/s of ethanol (cp = 2.44 kJ/(kg·K)) is heated from 35 to 60 °C. Find the heat transfer rate Q̇.

ṁ = 3 kg/scp = 2.44 kJ/(kg·K)T: 35 → 60 °C
Q̇ = kW
3.Medium
lengthT100 °C60 °C25 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 420 kW. The hot fluid cools from 100 to 60 °C and the cold fluid heats from 25 to 45 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 420 kWU = 1500 W/(m²·K)Th: 100 → 60 °CTc: 25 → 45 °C
A = m²
4.Medium
lengthT105 °C65 °C90 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 600 kW. The hot fluid cools from 105 to 65 °C and the cold fluid heats from 10 to 90 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 600 kWF = 0.92U = 500 W/(m²·K)Th: 105 → 65 °CTc: 10 → 90 °C
A = m²
5.Hard
lengthT135 °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 135 °C and the cold stream at 10 °C. The exchanger has A = 4 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 135 °CTc,in = 10 °CA = 4 m²U = 200 W/(m²·K)
Th,out = °C
6.Hard
lengthT175 °C140 °C29.44 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 175 to 140 °C in a counter-flow exchanger. It heats 2 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 = 2.3 kJ/(kg·K)Th: 175 → 140 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 155.1 kW
  2. 2. Q̇ = 183 kW
  3. 3. A = 7.511 m²
  4. 4. A = 42.37 m²
  5. 5. Th,out = 91.52 °C
  6. 6. A = 0.8943 m²

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