Heat Exchangers

Why it matters

Heat exchangers are essential in numerous industrial applications, including power plants, chemical processing, and HVAC systems. They enable efficient energy transfer, reducing energy consumption and operational costs.

Key ideas

• Definition: A heat exchanger is a device that transfers heat between two or more fluids at different temperatures.
• Types of Heat Exchangers:
  • Shell and Tube: One fluid flows inside tubes and the other on the shell side around the tubes.
  • Plate: Made up of multiple thin, slightly separated plates that have very large surface areas and fluid flow passages for heat transfer.
  • Air Cooled: Uses air to cool the fluid, often used in automotive and aerospace applications.
• Flow Arrangements:
  • Parallel Flow: Both fluids move in the same direction.
  • Counter Flow: Fluids move in opposite directions; for equal UA and capacity rates, ideal counterflow generally gives at least as high effectiveness as parallel flow.
  • Cross Flow: Fluids move perpendicular to each other.
• Effectiveness: A measure of the heat exchanger's ability to transfer heat, defined as the ratio of actual heat transfer to the maximum possible heat transfer.

Formulas

• Q = U·A·ΔT_m
  • Q: Heat transfer rate (W)
  • U: Overall heat transfer coefficient (W/m²·K)
  • A: Heat transfer area (m²)
  • ΔT_m: Log mean temperature difference (K)
• ΔT_m = (ΔT_1 - ΔT_2) / ln(ΔT_1/ΔT_2)
  • ΔT_1: Temperature difference at one end (K)
  • ΔT_2: Temperature difference at the other end (K)

For ideal steady parallel/counterflow with constant U, negligible ambient heat loss and appropriate constant heat capacities, Q = UA ΔT_lm. Multipass or crossflow arrangements may require a correction factor F. Keep U and A referenced to the same surface. Energy balance also requires Q = C_h(T_h,in-T_h,out) = C_c(T_c,out-T_c,in), where C = mdot c_p. Effectiveness ε = Q/[C_min(T_h,in-T_c,in)].

Worked example

Given: A counter-flow heat exchanger with hot fluid entering at 150°C and leaving at 100°C, and cold fluid entering at 30°C and leaving at 80°C. The overall heat transfer coefficient U is 500 W/m²·K, and the heat transfer area A is 10 m².

1. Calculate the log mean temperature difference (ΔT_m).

   • ΔT_1 = 150°C - 80°C = 70 K
   • ΔT_2 = 100°C - 30°C = 70 K
   • Both terminal differences are equal, so use the continuous limiting value ΔT_m = 70 K; direct substitution would give the indeterminate form 0/0.

2. Calculate the heat transfer rate (Q).

   • Q = U·A·ΔT_m
   • Q = 500 W/m²·K · 10 m² · 70 K
   • Q = 350,000 W

Final Answer: 350 kW. The given 50 K change in each stream implies C_h = C_c = 350/50 = 7 kW/K; mass flow rates and heat capacities must be consistent with these values.

Common mistakes

• Confusing the flow arrangements, especially parallel and counter flow.
• Incorrect calculation of the log mean temperature difference.
• Neglecting the units in calculations, leading to errors in the final result.

For GATE ME

Questions often involve calculating the heat transfer rate, effectiveness, or the log mean temperature difference. Practice problems on different types of heat exchangers and flow arrangements.

Quick check

1. What is the primary function of a heat exchanger?
2. Name two types of heat exchangers.
3. What is the formula for the log mean temperature difference?

Answers: 1. To transfer heat between fluids. 2. Shell and Tube, Plate. 3. (ΔT_1 - ΔT_2) / ln(ΔT_1/ΔT_2).