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.

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Heat transfer Additive manufacturing Low-order modelling
Not sure where to start? 4 places to go

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

Screening a heat exchanger before meshing: fix the allowable effectiveness and pressure drop; back out the required area and hydraulic diameter from correlated U and friction models; then check the layout against additive manufacturing limits: minimum feature size, overhangs, powder removal and roughness.SCREEN BEFORE YOU MESH[01]Fix the targetsallowable effectivenessand pressure drop[02]Back out the geometryrequired area and hydraulicdiameter, from U and friction[03]Check it can be printedfeature size, overhangs,powder removal, roughness
SCREEN BEFORE YOU MESH[01]Fix the targetsallowable effectivenessand pressure drop[02]Back out the geometryrequired area and hydraulicdiameter, from U and friction[03]Check it can be printedfeature size, overhangs,powder removal, roughness
The design use in three steps. The last one is what rejects a layout before powder is committed.

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 any two-stream exchanger, balanced or not. The functional form \(\varepsilon = f(\mathrm{NTU}, \dot{C}_r)\), with \(\dot{C}_r = \dot{C}_{\min}/\dot{C}_{\max}\), 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

The overall heat transfer coefficient U as three thermal resistances in series between the hot and cold streams: convection on the hot side, conduction through the wall set by its thickness and conductivity, and convection on the cold side, plus a contact resistance if the parts are bonded.OVERALL U AS RESISTANCES IN SERIESHOT STREAMCOLD STREAMconvectionhot sidewall conductionthickness, conductivityconvectioncold sideplus contact, if bonded
OVERALL U IN SERIESHOTCOLDconvectionhotconductionwallconvectioncoldplus contact resistance, if bonded
What goes into U, from the checklist below: each resistance is a line in the model that has to be documented.
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

Surface roughness, an effective roughness height treated as a sensitivity rather than a single constant, feeds both budgets. On one path it sets the relative roughness in the friction factor f, from Blasius or Colebrook-White, and so the pressure drop. On the other it enters the convective heat-transfer coefficient h, which sets the overall U through series resistances, then NTU as U A over C min, then the effectiveness as a function of NTU and C r. Validation checks the sensitivity of effectiveness and pressure drop to correlation choice and roughness.ONE ROUGHNESS, TWO BUDGETSSurfaceroughnesseffectiveroughness height,a sensitivity,not a singleconstantFriction factor fBlasius or Colebrook-White, relativeroughness from AM surface finishΔppressuredrophconvectiveHTCUseriesresistancesNTUUA / Cminεf(NTU, Cr)VALIDATION POSTUREthe sensitivity of ε and Δp to correlation choice and roughness
ONE ROUGHNESS, TWO BUDGETSSurface roughnesseffective roughness height, a sensitivity,not a single constantFriction factor fBlasius orColebrook-White,relative roughnessfrom AM surfacefinishΔppressure drophconvective HTCUseries resistancesNTUUA / Cminεf(NTU, Cr)VALIDATION POSTUREthe sensitivity of ε and Δp to correlationchoice and roughness
The checklist, the NTU framing and the AM limits joined up: the same roughness reaches both allowables the design fixes, which is why it is carried as a sensitivity.

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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