# Performance of tubular aluminum foam heat exchangers in multiple row bundles

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## Abstract

Two sets of aluminum foam cylinders, 5 and 15 mm thick, are being tested in two-row and three-row bundles for their thermo-hydraulic performance. The bundles are formed using fixed transversal and longitudinal pitch distances and subject to airflow between 0.5 and 5.0 at 0.5 m s^{−1} interval under cross-flow. The effects of foam layer thickness and the number of row under staggered configuration are investigated. Thermo-hydraulic results are benchmarking against those of a conventional finned tube bundle of similar dimensions with pre-determined number of fins and assembled using the same pitch distances.

## Keywords

Metal foams Heat exchangers Condensers Tube bank Tube bundle Cooling towers Cross-flow Geothermal## List of symbols

*A*Area (\(\hbox {m}^2\))

- \(\bar{c}_{\mathrm{p}}\)
Specific heat capacity at constant pressure (J kg

^{−1}K^{−1})- \(d_{\mathrm{f}}\)
Strut diameter (m)

- \(d_{\mathrm{i}}\)
Core tube internal diameter (m)

- \(d_{{\mathrm{o}}}\)
Core tube external diameter (m)

- \(D_{\mathrm{i}}\)
Foam or fin annulus internal diameter \(= d_{{\mathrm{o}}}\) (m)

- \(D_{\mathrm{o}}\)
Foam or fin annulus external diameter (m)

*f*Friction factor (–)

*H*Dimensional height (m)

*h*Convective heat transfer coefficient (W \(\hbox {m}^{-2}\) K

^{−1}])*Kp*Pressure loss coefficient (–)

*k*Thermal conductivity (W m

^{−1}K^{−1})*L*Dimensional length (m)

- \(\dot{m}\)
Mass flow rate (kg s

^{−1})*Nu*Nusselt number (–)

*P*Pressure (Pa)

- \(\dot{Q}\)
Heat transfer rate (W)

*R*Thermal resistance (K W

^{−1})*Re*Reynolds number (–)

- \(S_{\mathrm{L}}\)
Longitudinal pitch distance (m)

- \(S_{\mathrm{T}}\)
Transversal pitch distance (m)

- \(t_{\mathrm{f}}\)
Fin thickness (m)

- \(t_{\mathrm{p}}\)
Fin pitch (m)

*T*Temperature (K or \(^\circ\)C)

- \(\vec {u}\)
Air velocity (m s

^{−1})*U*Universal heat transfer coefficient (W \(\hbox {m}^{-2}\) K

^{−1})*W*Dimensional width (m)

- \(\hat{X}_{\mathrm{L}}\)
Ratio of longitudinal pitch to core diameter \(= S_{\mathrm{L}}/d_{\mathrm{o}}\) (–)

- \(\hat{X}_{\mathrm{T}}\)
Ratio of transversal pitch to core diameter \(= S_{\mathrm{T}}/d_{\mathrm{o}}\)(–)

## Abbreviations

- FS
Full scale

- HTC
Convective heat transfer coefficient (W \(\hbox {m}^{-2}\) K

^{−1})- LMTD
Log mean temperature difference (K or \(^\circ\)C)

- NTU
Number of transfer unit (–)

- PID
Proportional–integral–derivative feedback control

- PPI
Pores per inch [technically in\(^{-1}\), treated as (–)]

- RTD
Resistance temperature detector

- TCR
Thermal contact resistance (K/W)

## Greek symbols

- \(\Delta\)
Differential of

- \(\epsilon\)
Heat exchanger efficiency (–)

- \(\eta\)
Surface efficiency of aluminum foam (–)

- \(\mu\)
Dynamic viscosity (Pa s)

- \(\rho\)
Mass density (kg \(\hbox {m}^{-3}\))

- \(\phi\)
Porosity (–)

- \(\Omega ^*\)
Efficiency function of foam

## Common Subscripts

*a*Of the air

*c*Of the colder fluid taking up heat

*h*Of the hotter fluid losing heat

*i*Of inside surface

- max
The largest value

- min
The smallest value

*o*Of outside surface

*s*Of a surface

*t*Overall, total

- \(\infty\)
Of the bulk air free flow stream

## Notes

### Acknowledgements

The principal author is grateful to QGECE for its financial support to this study. Both authors also express their gratitude to the following individuals: Professor Thomas Rösgen for setting up the PIV facility, giving initial tutorials, and providing supervision on related works in his lab at the Institut Für Fluiddynamik, ETH-Zurich; Mostafa Odabaee for his help in sourcing test specimens; Dr Morteza Khashehchi, who helped process PIV data for velocity check; Joy Wang and Peter Bleakley for helping with data logging instrument; Douglas Malcolm for helping with wind tunnel operation and air velocity PID control program; and lastly Berto Di Pasquale for general fabrication of in-house parts and accessories.

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