Entrance length effects on Graetz number scaling in laminar duct flows with periodic obstructions: Transport number correlations for spacer-filled membrane channel flows
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Transport numbers scale with Graetz number for steady flows with periodic obstacles.

Thermal entrance length scales with Graetz number as in empty channel flows.

Beyond entrance length, transport numbers weakly depend on Reynolds and Prandtl.

Graetz number scaling breaks down with the onset of unsteady flow conditions.

Mass transfer in spacer-filled channel flows is dominated by entrance length effects.

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