Heat Exchangers

Why it matters

Heat exchangers are essential in numerous industrial applications, including power plants, chemical processing, and HVAC systems. They enable efficient thermal energy transfer, which is vital for optimizing energy use and reducing operational costs.

Key ideas

• Types of Heat Exchangers: Common types include shell-and-tube, plate, and finned-tube heat exchangers. Each type has specific applications based on factors like temperature, pressure, and fluid type.
• Flow Arrangements: The main flow arrangements are parallel flow, counterflow, and crossflow. For the same UA and capacity rates, ideal counterflow generally has at least as high effectiveness as parallel flow.
• Effectiveness: This is a measure of a heat exchanger's ability to transfer heat relative to the maximum possible heat transfer. It depends on the flow arrangement and the heat exchanger's design.
• Overall Heat Transfer Coefficient (U): This is a crucial parameter that combines the relevant fluid-film, wall and fouling resistances on a specified area basis. Radiation requires separate treatment when significant.

Formulas

• Q = U·A·ΔT_lm
  • Q: Heat transfer rate (W)
  • U: Overall heat transfer coefficient (W/m²·K)
  • A: Heat transfer area (m²)
  • ΔT_lm: Log mean temperature difference (K)
• ΔT_lm = (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)

Worked example

Given for an ideal steady counterflow exchanger with constant U and negligible heat loss to ambient:

• Hot fluid inlet temperature, T_h1 = 150°C
• Hot fluid outlet temperature, T_h2 = 100°C
• Cold fluid inlet temperature, T_c1 = 30°C
• Cold fluid outlet temperature, T_c2 = 80°C
• Overall heat transfer coefficient, U = 500 W/m²·K
• Heat transfer area, A = 10 m²

Steps:

1. Calculate ΔT_1 and ΔT_2:
   • ΔT_1 = T_h1 - T_c2 = 150°C - 80°C = 70°C
   • ΔT_2 = T_h2 - T_c1 = 100°C - 30°C = 70°C
2. Calculate ΔT_lm:
   • ΔT_lm = (ΔT_1 - ΔT_2) / ln(ΔT_1/ΔT_2)
   • The direct expression is 0/0; take its continuous limit when the two terminal differences are equal: ΔT_lm = 70 K.
3. Calculate Q:
   • Q = U·A·ΔT_lm
   • Q = 500 W/m²·K · 10 m² · 70 K
   • Q = 350,000 W

Final Answer: 350 kW. The 50 K changes imply both stream heat-capacity rates are 7 kW/K. U and A must refer to the same surface. Multipass/crossflow arrangements can require an LMTD correction factor.

Common mistakes

• Confusing the flow arrangements and their impact on heat transfer efficiency.
• Incorrect calculation of the log mean temperature difference, especially when ΔT_1 and ΔT_2 are similar.
• Neglecting the units in calculations, leading to incorrect results.

For GATE ME

Questions often involve calculating the heat transfer rate, effectiveness, or the overall heat transfer coefficient. Practice problems on different flow arrangements and their impact on performance.

Quick check

1. What is the most efficient flow arrangement in heat exchangers?
2. Define the overall heat transfer coefficient.
3. How does the log mean temperature difference affect heat transfer?

Answers: 1. Counterflow 2. An overall conductance per area combining relevant thermal resistances 3. It determines the driving force for heat transfer.