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
lengthT115 °C65 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 115 to 65 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 115 → 65 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
2.Easy
lengthT120 °C55 °C25 °C40 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 120 to 55 °C while the cold fluid heats from 25 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 55 °CTc: 25 → 40 °C
ΔTlm = K
3.Medium
lengthT125 °C75 °C25 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 600 kW. The hot fluid cools from 125 to 75 °C and the cold fluid heats from 10 to 25 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 600 kWF = 0.92U = 200 W/(m²·K)Th: 125 → 75 °CTc: 10 → 25 °C
A = m²
4.Medium
lengthT165 °C90 °C30 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 630 kW. The hot fluid cools from 165 to 90 °C and the cold fluid heats from 20 to 30 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 630 kWF = 0.95U = 500 W/(m²·K)Th: 165 → 90 °CTc: 20 → 30 °C
A = m²
5.Hard
lengthT170 °C110 °C65.89 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 170 to 110 °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. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 170 → 110 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT110 °C80 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.2 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 110 to 80 °C. Water (0.2 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 50 mm, and U = 300 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.2 kg/scp,h = 2.5 kJ/(kg·K)Th: 110 → 80 °Cṁc = 0.2 kg/sTc,in = 10 °CD = 50 mmU = 300 W/(m²·K)
L = m

Answer key

  1. 1. Tc,out = 54.9 °C
  2. 2. ΔTlm = 43.34 K
  3. 3. A = 40.14 m²
  4. 4. A = 13.4 m²
  5. 5. A = 8.194 m²
  6. 6. L = 4.196 m

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