Additive heat-exchanger low-order models

Compact correlations and NTU-effectiveness framing for screening metal additive-manufactured heat exchangers, assumptions, pressure-loss budgets, and manufacturability checks supporting the 2024 Engineering Research Express paper.

Heat transfer Additive manufacturing Low-order modelling
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Start with your question

Why visitors arrive: You are screening additive heat-exchanger concepts before CFD or build.

Your question: How do NTU-effectiveness and low-order correlations guide AM HX design?

You may also be asking

  • Where is the peer-reviewed publication?
  • What manufacturability constraints matter?
  • Which dimensionless groups apply?

Where to go next

Screen before you mesh

Low-order models do not replace validation, they narrow the design space. The goal is to reject non-viable channel layouts before powder is committed, while keeping every correlation and property input traceable.

NTU-effectiveness framing

For a two-stream heat exchanger with known heat capacity rates \(\dot{C}_h\) and \(\dot{C}_c\), the number of transfer units and effectiveness provide a compact design language:

\[ \mathrm{NTU} = \frac{U A}{\dot{C}_{\min}} \;,\qquad \varepsilon = \frac{Q}{Q_{\max}} \]

where \(U\) is the overall heat-transfer coefficient, \(A\) is the exchange area, and \(Q_{\max} = \dot{C}_{\min}(T_{h,\mathrm{in}} - T_{c,\mathrm{in}})\) for balanced definitions. The functional form \(\varepsilon = f(\mathrm{NTU}, \dot{C}_r)\) depends on flow arrangement (parallel, counter, cross), state the assumed configuration explicitly in any design note.

Design use: fix allowable \(\varepsilon\) and pressure drop, back out required \(A\) and hydraulic diameter from correlated \(U\) and friction models, then check against AM feature limits.

Correlation selection checklist

Quantity Typical low-order source Document in the model
Convective HTC \(h\) Dittus-Boelter, Gnielinski, or laminar tube correlations depending on Re, Pr, and entrance length Regime limits; property evaluation temperature; hydraulic diameter
Friction factor \(f\) Blasius / Colebrook-White branches for smooth and rough passages Relative roughness from AM surface finish assumptions
Overall \(U\) Series thermal resistances: convection-wall conduction-convection Wall thickness, solid conductivity, contact resistance if bonded
Fluid properties Temperature-dependent \(\rho\), \(\mu\), \(k\), \(c_p\) Film vs bulk temperature; link to air properties tool

Additive manufacturability constraints

A thermally attractive channel that cannot be printed, depowdered, or inspected is not a design. Low-order screening should include explicit AM checks:

  • Minimum feature size: channel width, wall thickness, lattice strut diameter vs machine resolution
  • Overhangs and supports: regions requiring sacrificial material that block flow or add thermal resistance
  • Powder removal: dead volumes that trap powder or prevent inspection
  • Surface roughness: feeds both \(\Delta p\) and \(h\) through effective roughness height, treat as a sensitivity, not a single constant

Applied context: DMLS camera housing project.

Validation posture

Low-order screening should name the validation step before results are quoted externally:

  1. Sensitivity of \(\varepsilon\) and \(\Delta p\) to correlation choice and roughness
  2. Targeted conjugate CFD on the surviving layout(s)
  3. Instrumented experiment with stated uncertainty, see measurement uncertainty fundamentals

Formal publication: Low-order-model-based design of additive-manufactured heat exchanger (DOI 10.1088/2631-8695/ad7cc4).

About this work

Lucas Rey, aerothermal systems engineer and academic tutor.

  • University of Oxford: DPhil Researcher, Thermofluids Institute.
  • University of Cambridge: Alumnus.
  • Rolls-Royce: Sponsored researcher (High-pressure turbine programme).

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