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
lengthT110 °C70 °C?15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 110 to 70 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 110 → 70 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
2.Easy
lengthT90 °C45 °C55 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 45 °C while the cold fluid heats from 20 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 45 °CTc: 20 → 55 °C
ΔTlm = K
3.Medium
lengthT170 °C145 °C110 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 90 kW. The hot fluid cools from 170 to 145 °C and the cold fluid heats from 10 to 110 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 90 kWU = 500 W/(m²·K)Th: 170 → 145 °CTc: 10 → 110 °C
A = m²
4.Medium
lengthT90 °C75 °C70 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 670 kW. The hot fluid cools from 90 to 75 °C and the cold fluid heats from 20 to 70 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 670 kWF = 0.9U = 200 W/(m²·K)Th: 90 → 75 °CTc: 20 → 70 °C
A = m²
5.Hard
lengthT120 °C30 °C23.46 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 30 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 30 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT160 °C90 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 160 to 90 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 20 mm, and U = 200 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 160 → 90 °Cṁc = 0.5 kg/sTc,in = 10 °CD = 20 mmU = 200 W/(m²·K)
L = m

Answer key

  1. 1. Tc,out = 59.02 °C
  2. 2. ΔTlm = 29.72 K
  3. 3. A = 1.946 m²
  4. 4. A = 107.6 m²
  5. 5. A = 1.543 m²
  6. 6. L = 60.69 m

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