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 °C85 °C15 °C45 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 140 to 85 °C while the cold fluid heats from 15 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 85 °CTc: 15 → 45 °C
ΔTlm = K
2.Easy
lengthT170 °C55 °C115 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 170 to 55 °C while the cold fluid heats from 10 to 115 °C. Find the log-mean temperature difference ΔTlm.

Th: 170 → 55 °CTc: 10 → 115 °C
ΔTlm = K
3.Medium
lengthT100 °C20 °C60 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °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 20 to 60 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 60 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT105 °C25 °C55 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 110 kW. The hot fluid cools from 105 to 25 °C and the cold fluid heats from 10 to 55 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 110 kWU = 200 W/(m²·K)Th: 105 → 25 °CTc: 10 → 55 °C
A = m²
5.Hard
lengthT120 °C65 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-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 120 to 65 °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 = 250 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: 120 → 65 °Cṁc = 0.2 kg/sTc,in = 10 °CD = 50 mmU = 250 W/(m²·K)
L = m
6.Hard
lengthT135 °C??25 °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 135 °C and the cold stream at 25 °C. The exchanger has A = 6 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 135 °CTc,in = 25 °CA = 6 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 74.6 K
  2. 2. ΔTlm = 49.83 K
  3. 3. A = 4.139 m²
  4. 4. A = 18.92 m²
  5. 5. L = 14.34 m
  6. 6. Th,out = 93.75 °C

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