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 °C60 °C125 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 6 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 140 to 60 °C and the cold fluid heats from 15 to 125 °C. Find the heat transfer rate Q̇.

A = 6 m²U = 800 W/(m²·K)Th: 140 → 60 °CTc: 15 → 125 °C
Q̇ = kW
2.Easy
lengthT140 °C80 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 140 to 80 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 140 → 80 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
3.Medium
lengthT100 °C15 °C40 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 15 to 40 °C. The overall heat transfer coefficient is 2500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 15 → 40 °CU = 2500 W/(m²·K)
A = m²
4.Medium
lengthT140 °C20 °C105 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 105 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 105 °CU = 3500 W/(m²·K)
A = m²
5.Hard
lengthT120 °C??30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 120 °C and the cold stream at 30 °C. The exchanger has A = 4 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 120 °CTc,in = 30 °CA = 4 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT150 °C65 °C116.7 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 150 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 = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 150 → 65 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 131.1 kW
  2. 2. Tc,out = 58.01 °C
  3. 3. A = 1.747 m²
  4. 4. A = 2.943 m²
  5. 5. Th,out = 68.57 °C
  6. 6. A = 34.47 m²

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