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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
lengthT115 °C55 °C75 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 55 °C while the cold fluid heats from 20 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 55 °CTc: 20 → 75 °C
ΔTlm = K
2.Easy

In a heat exchanger 2.5 kg/s of ethanol (cp = 2.44 kJ/(kg·K)) is cooled from 100 to 45 °C. Find the heat transfer rate Q̇.

ṁ = 2.5 kg/scp = 2.44 kJ/(kg·K)T: 100 → 45 °C
Q̇ = kW
3.Medium
lengthT165 °C145 °C90 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 490 kW. The hot fluid cools from 165 to 145 °C and the cold fluid heats from 25 to 90 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 490 kWU = 200 W/(m²·K)Th: 165 → 145 °CTc: 25 → 90 °C
A = m²
4.Medium
lengthT110 °C25 °C40 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 110 °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 40 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 110 °Cṁ = 4 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 40 °CU = 3500 W/(m²·K)
A = m²
5.Hard
lengthT155 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 155 °C and the cold stream at 15 °C. The exchanger has A = 3 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 155 °CTc,in = 15 °CA = 3 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT150 °C120 °C37.01 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 150 to 120 °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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 150 → 120 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 37.44 K
  2. 2. Q̇ = 335.5 kW
  3. 3. A = 25.59 m²
  4. 4. A = 0.9275 m²
  5. 5. Th,out = 71 °C
  6. 6. A = 1.583 m²

Full step-by-step solutions: practise this topic on examproblems.com.