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
lengthT80 °C40 °C40 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 15 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 80 to 40 °C and the cold fluid heats from 20 to 40 °C. Find the heat transfer rate Q̇.

A = 15 m²U = 500 W/(m²·K)Th: 80 → 40 °CTc: 20 → 40 °C
Q̇ = kW
2.Easy
lengthT120 °C55 °C?10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 120 to 55 °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 = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 120 → 55 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
3.Medium
lengthT110 °C25 °C50 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 110 °C on the outside of the tubes. Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 25 to 50 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 110 °Cṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 50 °CU = 3000 W/(m²·K)
A = m²
4.Medium
lengthT125 °C105 °C15 °C80 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 490 kW. Its heat transfer area is 3 m². The hot fluid cools from 125 to 105 °C and the cold fluid heats from 15 to 80 °C. Find the overall heat transfer coefficient U.

Q̇ = 490 kWA = 3 m²Th: 125 → 105 °CTc: 15 → 80 °C
U = W/(m²·K)
5.Hard
lengthT140 °C70 °C?25 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 140 to 70 °C. Water (0.2 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 25 °C. The inner tube has a diameter of 32 mm, and U = 400 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 140 → 70 °Cṁc = 0.2 kg/sTc,in = 25 °CD = 32 mmU = 400 W/(m²·K)
L = m
6.Hard
lengthT130 °C60 °C15 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 130 to 60 °C. Water (1 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 50 mm, and U = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.3 kJ/(kg·K)Th: 130 → 60 °Cṁc = 1 kg/sTc,in = 15 °CD = 50 mmU = 250 W/(m²·K)
L = m

Answer key

  1. 1. Q̇ = 216.4 kW
  2. 2. Tc,out = 15.96 °C
  3. 3. A = 0.9706 m²
  4. 4. U = 2847 W/(m²·K)
  5. 5. L = 66.83 m
  6. 6. L = 18.63 m

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