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TECHNICAL PAPERS: Porous Media

# Convective Heat Transfer in Open Cell Metal Foams

[+] Author and Article Information
Ken I. Salas1

Department of Aerospace Engineering,  The University of Michigan, Ann Arbor, MI 48109

Anthony M. Waas2

Department of Aerospace Engineering,  The University of Michigan, Ann Arbor, MI 48109

1

E-mail: ksalas@umich.edu

2

Corresponding author. e-mail: dcw@umich.edu

J. Heat Transfer 129(9), 1217-1229 (Dec 08, 2006) (13 pages) doi:10.1115/1.2739598 History: Received March 26, 2006; Revised December 08, 2006

## Abstract

Convective heat transfer in aluminum metal foam sandwich panels is investigated with potential applications to actively cooled thermal protection systems in hypersonic and re-entry vehicles. The size effects of the metal foam core are experimentally investigated and the effects of foam thickness on convective transfer are established. Four metal foam specimens are utilized with a relative density of 0.08 and pore density of 20 pores per inch (ppi) in a range of thickness from $6.4mmto25.4mm$, in increments of approximately $6mm$. An exact-shape-function finite element model is developed that envisions the foam as randomly oriented cylinders in cross flow with an axially varying coolant temperature field. A fully developed velocity profile is obtained through a semi-empirical, volume-averaged form of the momentum equation for flow through porous media, and used in the numerical analysis. The experimental results show that larger foam thicknesses produce increased heat transfer levels, but that this effect diminishes for thicker foams. The finite element simulations capture the thickness dependence of the heat transfer process and good agreement between experimental and numerical results is obtained for larger foam thicknesses.

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## Figures

Figure 1

Geometry of a sample metal foam sandwich panel used in the present study. The specimen shown has a foam thickness of 6.4mm and a face sheet thickness of approximately 1.1mm.

Figure 2

Detail of fully insulated metal foam sandwich panel specimen

Figure 3

Detail of heated surface in metal foam sandwich panel specimen. Each heater has dimensions of 76mm long by 15mm wide.

Figure 4

Diagram of experimental setup

Figure 5

Sample thermocouple readings for heated side. The air velocity is 12.1m∕s, the foam thickness is 12.7mm, and the voltage setting is 22V resulting in a heat flux of 730W∕m2.

Figure 6

Sample thermocouple readings for insulated side. The air velocity is 12.1m∕s, the foam thickness is 12.7mm, and the voltage setting is 22V, resulting in a heat flux of 730W∕m2.

Figure 7

Effect of thickness on temperature difference across metal foam. The voltage setting was kept constant in all cases at 22V resulting in a heat flux of 730W∕m2.

Figure 8

Dependence of average convection coefficient of metal foam on foam thickness. The voltage setting was kept constant in all cases at 22V resulting in a heat flux of 730W∕m2.

Figure 9

Nondimensional average convection coefficient of metal foam. Re and Nu calculated based on foam thickness. The voltage setting was kept constant in all cases at 22V resulting in a heat flux of 730W∕m2.

Figure 10

Pressure drop across 6.4‐mm-thick metal foam core

Figure 11

Pressure drop across 12.7‐mm-thick metal foam core

Figure 12

Pressure drop across 25.4‐mm-thick metal foam core

Figure 13

Geometry of metal foam sandwich panel used in nondimesionalization of momentum equation

Figure 14

Sample velocity profile across metal foam

Figure 15

Decomposition of flow velocity into parallel and perpendicular components with respect to cylinder axis

Figure 16

Illustration of sample through-the-thickness cylinder arrangement used in finite element simulations for each axial section

Figure 17

Comparison of finite element model prediction and experimental results for temperature distribution on sandwich panel. The foam thickness is 6.4mm, the air velocity is 17.6m∕s, and the voltage setting is 22V resulting in an applied heat flux of 730W∕m2. Random cylinder orientation.

Figure 18

Comparison of finite element model prediction and experimental results for temperature distribution on sandwich panel. The foam thickness is 12.7mm, the air velocity is 5.9m∕s, and the voltage setting is 22V resulting in an applied heat flux of 730W∕m2. Random cylinder orientation.

Figure 19

Comparison of finite element model prediction and experimental results for temperature distribution on sandwich panel. The foam thickness is 19.0mm, the air velocity is 5.8m∕s, and the voltage setting is 22V resulting in an applied heat flux of 730W∕m2. Random cylinder orientation.

Figure 20

Comparison of finite element model prediction and experimental results for temperature distribution on sandwich panel. The foam thickness is 25.4mm, the air velocity is 2.9m∕s, and the voltage setting is 22V resulting in an applied heat flux of 730W∕m2. Random cylinder orientation.

Figure 21

Effect of varying cylinder angle on model prediction. The foam thickness is 25.4mm, the air velocity is 2.9m∕s, and the voltage setting is 22V resulting in a heat flux of 730W∕m2. Heated side.

Figure 22

Effect of varying cylinder angle on model prediction. The foam thickness is 25.4mm, the air velocity is 2.9m∕s, and the voltage setting is 22V resulting in a heat flux of 730W∕m2. Insulated side.

Figure 23

Effect of varying cylinder angle on model prediction. The foam thickness is 6.4mm, the air velocity is 17.6m∕s, and the voltage setting is 22V resulting in a heat flux of 730W∕m2. Heated side.

Figure 24

Effect of varying cylinder angle on model prediction. The foam thickness is 6.4mm, the air velocity is 17.6m∕s, and the voltage setting is 22V resulting in a heat flux of 730W∕m2. Insulated side.

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