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
lengthT160 °C110 °C?10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 160 to 110 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °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: 160 → 110 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
2.Easy
lengthT165 °C105 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 165 to 105 °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 = 2.5 kJ/(kg·K)Th: 165 → 105 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
3.Medium
lengthT170 °C140 °C55 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 450 kW. The hot fluid cools from 170 to 140 °C and the cold fluid heats from 30 to 55 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 450 kWU = 1000 W/(m²·K)Th: 170 → 140 °CTc: 30 → 55 °C
A = m²
4.Medium
lengthT130 °C105 °C60 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 100 kW. The hot fluid cools from 130 to 105 °C and the cold fluid heats from 30 to 60 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 100 kWF = 0.88U = 200 W/(m²·K)Th: 130 → 105 °CTc: 30 → 60 °C
A = m²
5.Hard
lengthT145 °C110 °C20 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 145 to 110 °C. Water (0.3 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °C. The inner tube has a diameter of 50 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 145 → 110 °Cṁc = 0.3 kg/sTc,in = 20 °CD = 50 mmU = 500 W/(m²·K)
L = m
6.Hard
lengthT115 °C35 °C55.19 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 115 to 35 °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 = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 115 → 35 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 29.94 °C
  2. 2. Tc,out = 77.85 °C
  3. 3. A = 4.001 m²
  4. 4. A = 7.84 m²
  5. 5. L = 2.915 m
  6. 6. A = 30.82 m²

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