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 (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 140 to 80 °C in a counter-flow exchanger. It heats 3 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 = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 140 → 80 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
2.Easy
lengthT120 °C65 °C100 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 65 °C while the cold fluid heats from 25 to 100 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 65 °CTc: 25 → 100 °C
ΔTlm = K
3.Medium
lengthT90 °C40 °C60 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 560 kW. The hot fluid cools from 90 to 40 °C and the cold fluid heats from 15 to 60 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 560 kWF = 0.9U = 1000 W/(m²·K)Th: 90 → 40 °CTc: 15 → 60 °C
A = m²
4.Medium
lengthT140 °C50 °C65 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 470 kW. The hot fluid cools from 140 to 50 °C and the cold fluid heats from 20 to 65 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 470 kWU = 300 W/(m²·K)Th: 140 → 50 °CTc: 20 → 65 °C
A = m²
5.Hard
lengthT130 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 4 kW/K. The hot stream enters at 130 °C and the cold stream at 25 °C. The exchanger has A = 6 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 4 kW/KTh,in = 130 °CTc,in = 25 °CA = 6 m²U = 300 W/(m²·K)
Th,out = °C
6.Hard
lengthT180 °C60 °C35.1 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 180 to 60 °C in a counter-flow exchanger. It heats 1.5 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 = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 180 → 60 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 43.92 °C
  2. 2. ΔTlm = 28.85 K
  3. 3. A = 22.69 m²
  4. 4. A = 31.9 m²
  5. 5. Th,out = 97.41 °C
  6. 6. A = 1.844 m²

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