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 °C85 °C85 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 110 to 85 °C while the cold fluid heats from 25 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 85 °CTc: 25 → 85 °C
ΔTlm = K
2.Easy
lengthT135 °C40 °C50 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 40 °C while the cold fluid heats from 15 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 40 °CTc: 15 → 50 °C
ΔTlm = K
3.Medium
lengthT125 °C100 °C65 °C20 °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 100 °C and the cold fluid heats from 20 to 65 °C. The LMTD correction factor for this arrangement is F = 0.85, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 600 kWF = 0.85U = 1000 W/(m²·K)Th: 125 → 100 °CTc: 20 → 65 °C
A = m²
4.Medium
lengthT120 °C20 °C35 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °C on the outside of the tubes. Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 35 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 35 °CU = 1500 W/(m²·K)
A = m²
5.Hard
lengthT125 °C90 °C?20 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 125 to 90 °C. Water (0.8 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °C. The inner tube has a diameter of 32 mm, and U = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 125 → 90 °Cṁc = 0.8 kg/sTc,in = 20 °CD = 32 mmU = 250 W/(m²·K)
L = m
6.Hard
lengthT105 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 105 °C and the cold stream at 15 °C. The exchanger has A = 3 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 105 °CTc,in = 15 °CA = 3 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 39.98 K
  2. 2. ΔTlm = 49.03 K
  3. 3. A = 10.15 m²
  4. 4. A = 0.2264 m²
  5. 5. L = 19.79 m
  6. 6. Th,out = 84.23 °C

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