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
lengthT175 °C100 °C130 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 100 °C while the cold fluid heats from 10 to 130 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 100 °CTc: 10 → 130 °C
ΔTlm = K
2.Easy
lengthT110 °C80 °C50 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 110 to 80 °C and the cold fluid heats from 30 to 50 °C. Find the heat transfer rate Q̇.

A = 2 m²U = 800 W/(m²·K)Th: 110 → 80 °CTc: 30 → 50 °C
Q̇ = kW
3.Medium
lengthT120 °C10 °C80 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °C on the outside of the tubes. Cooling water (5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 80 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 80 °CU = 1500 W/(m²·K)
A = m²
4.Medium
lengthT170 °C80 °C120 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 660 kW. The hot fluid cools from 170 to 80 °C and the cold fluid heats from 20 to 120 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 660 kWF = 0.92U = 800 W/(m²·K)Th: 170 → 80 °CTc: 20 → 120 °C
A = m²
5.Hard
lengthT145 °C70 °C25 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 145 to 70 °C. Water (1 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 25 °C. The inner tube has a diameter of 25 mm, and U = 400 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 145 → 70 °Cṁc = 1 kg/sTc,in = 25 °CD = 25 mmU = 400 W/(m²·K)
L = m
6.Hard
lengthT165 °C115 °C74.81 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 165 to 115 °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. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 165 → 115 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 64.92 K
  2. 2. Q̇ = 87.76 kW
  3. 3. A = 14.09 m²
  4. 4. A = 16.35 m²
  5. 5. L = 22.13 m
  6. 6. A = 1.645 m²

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