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
lengthT140 °C80 °C?20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 140 to 80 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °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: 140 → 80 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
2.Easy
lengthT180 °C155 °C30 °C145 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 180 to 155 °C while the cold fluid heats from 30 to 145 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 155 °CTc: 30 → 145 °C
ΔTlm = K
3.Medium
lengthT175 °C105 °C70 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 380 kW. The hot fluid cools from 175 to 105 °C and the cold fluid heats from 15 to 70 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 380 kWU = 800 W/(m²·K)Th: 175 → 105 °CTc: 15 → 70 °C
A = m²
4.Medium
lengthT125 °C75 °C45 °C25 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 670 kW. The hot fluid cools from 125 to 75 °C and the cold fluid heats from 25 to 45 °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: 125 → 75 °CTc: 25 → 45 °C
A = m²
5.Hard
lengthT145 °C65 °C55.19 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 145 to 65 °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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 145 → 65 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT135 °C95 °C101.8 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 135 to 95 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 135 → 95 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 43.92 °C
  2. 2. ΔTlm = 51.7 K
  3. 3. A = 4.881 m²
  4. 4. A = 58.32 m²
  5. 5. A = 3.089 m²
  6. 6. A = 2.112 m²

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