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
lengthT175 °C115 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 175 to 115 °C in a counter-flow exchanger. It heats 1 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 = 2.5 kJ/(kg·K)Th: 175 → 115 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
2.Easy
lengthT165 °C95 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 165 to 95 °C in a counter-flow exchanger. It heats 1 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 = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 165 → 95 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
3.Medium
lengthT130 °C115 °C30 °C100 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 110 kW. The hot fluid cools from 130 to 115 °C and the cold fluid heats from 30 to 100 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 110 kWU = 1000 W/(m²·K)Th: 130 → 115 °CTc: 30 → 100 °C
A = m²
4.Medium
lengthT165 °C145 °C120 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 350 kW. The hot fluid cools from 165 to 145 °C and the cold fluid heats from 20 to 120 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 350 kWF = 0.9U = 300 W/(m²·K)Th: 165 → 145 °CTc: 20 → 120 °C
A = m²
5.Hard
lengthT110 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 110 °C on the outside of the tubes of a condenser with a heat transfer area of 6 m² and U = 2500 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 6 m²U = 2500 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT110 °C60 °C59.86 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 110 to 60 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 110 → 60 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 101.8 °C
  2. 2. Tc,out = 50.93 °C
  3. 3. A = 2.455 m²
  4. 4. A = 16.55 m²
  5. 5. Tc,out = 82.79 °C
  6. 6. A = 7.891 m²

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