About this note
A plain-language summary of the 6 publications listed under this topic on Academic Publications (Topic-wise). Full citations are under References.
Why this matters
A heat exchanger or heat sink removes heat by letting a cooling fluid sweep past a hot surface. The rate of heat removal depends on the surface area in contact with the fluid and on the convection heat transfer coefficient, which says how effectively the moving fluid picks up heat from each square metre of that surface. Filling part of the flow path with a porous medium (a solid matrix full of interconnected pores, such as a metal foam, a sintered layer or a wire mesh) raises both at once. The solid matrix adds an enormous wetted area, and the tortuous paths through the pores stir the fluid.
The catch is pressure drop: a porous insert also resists the flow, so more pumping power is needed. The useful question is therefore never “does the porous medium increase heat transfer?” but “is the extra heat transfer worth the extra pumping power?” That trade-off runs through every study summarised here.
What we did
Laying the foundations
The research line began with a review chapter written with José Lage at Southern Methodist University (Lage and Narasimhan, 2000). After setting out the fundamentals of forced convection through porous media, it surveyed post-1993 applications in five groups: porous inserts and cavities, microsintering with porous fins and coatings, microchannels, permeable fences and perforated baffles, and cylinder arrays. A central argument of the chapter is that porous-medium thinking can be applied usefully even to structures that do not look like a classic porous medium, such as an array of cylinders in cross flow.
One application discussed at length was a thin aluminium-foam-filled channel, a microporous enhanced cold plate, designed to cool phased-array radar antennas on military aircraft, where the porous insert both enhances convection and spreads the flow uniformly across the channel. Such compressed aluminium foam inserts were shown to behave hydraulically like a porous medium, characterised by their permeability (a measure of how easily fluid passes through a porous material) and form coefficient (which captures the extra drag from flow around the solid structure at higher speeds). A follow-up chapter (Lage et al., 2004) reported an experimental study of forced convection through such microporous enhanced heat sinks; its source was not available for this summary, so its specific results are not described here.
Treating a heat exchanger as a porous medium
At IIT Madras, with doctoral student K. Sumithra Raju, we turned the idea around. Instead of only putting a porous medium inside a heat exchanger, we treated a whole near-compact heat exchanger (a bank of small tubes, 2 mm in diameter, with a surface-to-volume ratio of 100 to 300 m²/m³) as a “global” porous medium. Its overall behaviour was then shaped by “local” porous inter-connectors: strips of metal foam linking each tube to the next along the flow direction (Raju and Narasimhan, 2007). Using numerical simulations of laminar air-like flow (Prandtl number 0.7, Reynolds number 10 to 100), we varied the thickness and permeability of these foam strips and tracked the overall Nusselt number (a dimensionless heat transfer coefficient) and a dimensionless pressure drop.
A companion study asked what happens if the foam’s permeability is not uniform but changes along the flow, from open to tight or from tight to open (Narasimhan and Raju, 2007).
Testing it in the laboratory
With P. V. Ramana and Dhiman Chatterjee, we built a confined bank of six heated tubes (9 mm diameter) in in-line and staggered arrangements, joined the tubes with brazed copper porous inter-connectors, and measured pressure drop and heat transfer, first with air in the laminar to transitional range (Ramana et al., 2010) and later with water in the laminar range (Ramana et al., 2012).
What we found
Heat exchangers can be described with a few porous-medium numbers. Treating the tube bank as a global porous medium worked well. Both the pressure drop and the heat transfer could be expressed through a single global Darcy number (a dimensionless permeability of the whole exchanger), which in turn depends on the thickness and permeability of the inter-connecting foam. The resulting design correlations predicted the simulated data within ±20% (Raju and Narasimhan, 2007). With graded-permeability foams, the correlations improved to within ±6%, the heat transfer of the graded cases fell between the two uniform-permeability limits, and at higher flow rates (Reynolds number above 70) a foam that went from tight to open along the flow gave less pressure drop than the most permeable uniform foam. The overall enhancement ratio, which weighs heat transfer gained against pumping power spent, rose as the foam became more permeable (Narasimhan and Raju, 2007).
Arrangement decides whether the trade is worth it. The experiments showed that the same inter-connector behaves very differently in the two tube layouts. In the in-line bank, the foam curtailed the recirculating vortices that normally sit in the gaps between tubes, so the pressure drop actually fell: by 18% at the highest air flow tested (Ramana et al., 2010) and by about 12% with water (Ramana et al., 2012), while the heat transfer gain was only marginal. In the staggered bank the picture reversed. Heat transfer rose substantially (a 70% increase across the air tests, reaching 100% at the highest flow, and about 50% with water), but the pressure drop roughly tripled. When the two effects were combined into an overall energy gain, the in-line arrangement with porous inter-connectors came out ahead (Ramana et al., 2010; Ramana et al., 2012).
Contact matters. Our simulations of the in-line water case predicted about three times more heat transfer than the experiments showed. Adding a thin, poorly conducting layer at the brazed joint between tube and foam brought the predictions into line with the measurements: thermal contact resistance was why the in-line enhancement stayed marginal (Ramana et al., 2012).
The field still needs better properties. The review concluded that designing porous-enhanced heat exchangers was then “more art than science”: the transport equations exist, but the properties needed to solve them, such as effective thermal conductivity and effective viscosity, are mostly unknown outside simple geometries like packed beds of spheres. It argued that porous-medium concepts should be applied more vigorously to irregular, non-uniform enhancing devices (Lage and Narasimhan, 2000), a call the later tube-bank studies took up.
Related
- Essentials of Heat and Fluid Flow in Porous Media
- Hydrodynamics in Porous Media, on measuring permeability and form coefficient, the two properties these designs depend on
- Turbulent Flows and Convection, on pressure drop in near-compact heat exchanger models treated as porous media
- Bi-disperse Porous Media
References
- Ramana, P. V., Narasimhan, A. and Chatterjee, D., (2012), “Thermo-Hydraulics of Tube Banks with Porous Interconnectors using Water as Cooling Fluid,” Frontiers in Heat and Mass Transfer, 3 (2), 023007. [DOI: 10.5098/hmt.v3.2.3007 | Abstract | PDF Download ]
- Ramana, P. V., Narasimhan, A. and Chatterjee, D., (2010), “Experimental Investigation of the Effect of Tube-to-tube Porous Medium Inter-connectors on the Thermo-hydraulics of Confined Tube Banks”, Heat Transfer Engg., 31, 1-9. [DOI 10.1080/01457630903412161]
- Narasimhan, A. and Raju, S. K., (2007), “Effect of Variable Permeability Porous Medium Inter-connectors on the Thermo-hydraulics of Heat Exchanger Modelled as Porous Media”, Int. J. Heat and Mass Transfer, 50, 4052-4062. [DOI 10.1016/S0096-3003(02)00635-5]
- Raju, S. K. and Narasimhan, A., (2007), “Porous Medium Inter-connector Effects on the Thermo-Hydraulics of Near-Compact Heat Exchangers treated as Porous Media”, ASME J. Heat Transfer, 129, 273-281. [DOI 10.1115/1.2427074]
- Lage, J. L., Narasimhan, A., Porneala, D. C. and Price, D. C., (2004), “Experimental Study of Forced Convection through Microporous Enhanced Heat Sinks” Emerging Technologies and Techniques in Porous Media, (Ed. D. B. Ingham et al.), Kluwer Acad. Pub., Netherlands, 28, 433-452.
- Lage, J. L. and Narasimhan, A., (2000), “Porous Media Enhanced Forced Convection: Fundamentals and Applications” in Handbook of Porous Media, (Ed. K. Vafai), 8, 357-394, Marcel Dekker pub., NY.