Heat Exchangers Notes

Introduction to Heat Exchangers

• Application of heat transfer principles is crucial in equipment design for product development aimed at economic gain.
• Economics ultimately influence the design and selection of heat-exchange equipment.
• In aerospace or space applications, weight and size are pivotal, often subordinating cost considerations.
• The design rules depend on the specific application and must consider various economic and physical factors.

Overview of Heat Exchanger Analysis

• The discussion will focus on technical analysis to predict heat-exchanger performance and methods to estimate size and type for specific tasks.
• Consideration of primary modes of heat transfer: conduction and convection (radiation also plays a role in certain applications).

The Overall Heat-Transfer Coefficient

• Defined: The overall heat-transfer coefficient (
  $U$)
  ) relates to heat transfer in the context of a heat exchanger configuration.
• In a plane wall heat exchanger: q = rac{TA - TB}{rac{1}{h1 A} + rac{ar{x}}{k A} + rac{1}{h2 A}}
  • Where:
  • $T<em>A$ and $T</em>B$ are fluid temperatures,
  • $h<em>1$ and $h</em>2$ are heat transfer coefficients,
  • ar{x} is the thickness of the wall,
  • $k$ is the thermal conductivity.
• For double-pipe heat exchangers, $q$ can be observed using a thermal-resistance approach: q = rac{TA - TB}{rac{1}{hi A} + rac{ ext{ln}(ro/ri)}{2 rans{π} k L} + rac{1}{ho A}} where:
  • $r<em>o$ and $r</em>i$ are the outer and inner pipe radius respectively,
  • $L$ is the length of the pipe.

Approximate Values of Overall Heat-Transfer Coefficients

• Provide tabulated data with values for different physical configurations and their respective heat transfer coefficients:
  • Examples include:
    | Physical Situation | $U$ (Btu/h · ft² · °F) | $U$ (W/m² · °C) |
    |--------------------|--------------------------|--------------------|
    | Brick wall, uninsulated | 0.45 | 2.55 |
    | Single plate-glass window | 1.10 | 6.2 |
    | Steam condenser | 200–1000 | 1100–5600 |
  • These values help guide the selection of appropriate heat exchangers for specific tasks.

Fouling Factors

• Fouling layers or corrosion can create additional thermal resistance, reducing heat exchanger efficiency.
• Fouling factors $R<em>f$ are derived from the clean and dirty conditions of the heat exchanger performance: Rf = rac{1}{U{dirty}} - rac{1}{U{clean}}
• Ensuring that fouling factors are accounted for during design is critical to maintaining performance.

Types of Heat Exchangers

1. Double-pipe heat exchangers
   • Simple design, allows for either counterflow or parallel flow.
2. Shell-and-tube heat exchangers
   • Common in the chemical-processing industry, utilizes baffles to direct the shell-side fluid across the tubes facilitating better heat transfer.
3. Cross-flow heat exchangers
   • Often used for gas heating/cooling.
   • The behavior of mixed vs unmixed fluids has significant implications on the overall heat transfer rates and efficiencies.
4. Compact heat exchangers
   • Designed for applications requiring high surface area within a small volume, typically seen in gas-flow environments where low overall heat transfer coefficients are common.

Log Mean Temperature Difference (LMTD)

• Utilizes the temperature variations in heat exchangers:
  • $q = UA imes ΔT_m$
• $ΔT_m$ is determined using either counterflow or parallel flow temperature profiles:
  • ΔTm = rac{(T{h,in} - T{c,out}) - (T{h,out} - T{c,in})}{ ext{ln} rac{(T{h,in} - T{c,out})}{(T{h,out} - T_{c,in})}}
  • Important for sizing and selecting heat exchangers in thermal systems.

Effectiveness-NTU Method

• An alternative to the LMTD method, beneficial for scenarios where outlet temperatures are unknown.
• Effectiveness (
  $ext{ε}$)
  , defined as the ratio of actual heat transfer to maximum possible heat transfer, is utilized in terms of NTU:
• Various formulas are available for different configurations (parallel flow, counterflow, cross-flow) that describe this relationship mathematically.