The effects of chaotic advection on heat transfer

Interfacial mass transport in steady three-dimensional flows in microchannels

“…While a specific value of Sh ∞ stat cannot be defined in these cases due to the continuing decrease of Sh(Z), it is instructive to note that Sh(Z) is similar in magnitude for the chaotic and non-chaotic flows. As noted by others (Acharya et al 2001, Ghosh et al 1998, Kirtland et al 2006, Mokrani et al 1997, Peerhossaini et al 1993, from a globally averaged Sherwood number or from a total integrated flux over the entire reactive interface, it is very difficult to distinguish the transport process in figure 6(a) from that in figure 6(b). The non-chaotic flow fails to exhibit modified Graetz behaviour for Pe > 10 5 , but this failure is subtle in the sense that in many cases it would not even be measurable from an external, global measurement.…”

“…Heat and mass transfer to solid-liquid interfaces and across liquid-liquid interfaces are fundamental to heat exchanger design (Acharya et al 1992, 2001, Mokrani et al 1997, Peerhossaini et al 1993, electrochemical systems for analysis and energy production (Cohen et al 2005, Ferrigno et al 2002, Shrivastava et al 2008, separations with membranes (Shrivastava et al 2008) and without membranes (Aref andJones 1989, Brody andYager 1997), fabrication at fluid-fluid interfaces (Kenis et al 1999, and sensors involving interfacial reactions (Foley et al 2008, Golden et al 2007, Kamholz et al 1999, Squires et al 2008, Teles and Fonseca 2008, Vijayendran et al 2003. Many of these systems rely on the suppression of turbulence as a means of controlling fluid flow, whereas others are relegated to laminar flow by other constraints.…”

“…Researchers working with Dean's flows in coiled tubes have cited enhanced heat transfer due to chaos (Peerhossaini et al 1993), although the increases in rates of transfer are relatively small in magnitude (13-27%, Mokrani et al 1997) and in scaling with the Prandtl number, Pr = ν/α, where ν is kinematic viscosity and α is thermal diffusivity (Pr 0.09 , Acharya et al 2001). For transport to the surface of confocal ellipses, a 100% increase over conduction is observed by Saatdjian et al (1996).…”

“…Finally, Shrivastava et al (2008) were able to predict to within 4-12% the enhancements seen in experiments with ultrafiltration membrane spacers using a simple model, even though this model assumes instantaneous mixing of the fluid. While it is difficult to incorporate the many experimental, numerical and theoretical results available in the literature into a single conclusion, a theme emerges: chaos can lead to significant increases in transfer to moving interfaces and internal, fluid-fluid interfaces (Bryden and Brenner 1999, Ganesan et al 1997, Lefevre et al 2003, while for transfer to solid, stationary interfaces, chaos leads to little or no increase in rates relative to analogous, nonchaotic flows (Acharya et al 2001, Ghosh et al 1998, Kirtland et al 2006, Mokrani et al 1997, Peerhossaini et al 1993.…”

Laminar mixing and heat transfer for constant heat flux boundary condition

“…Even if the flow in these pipes is steady, the chaotic character is obtained by elbows succession, where at sufficiently high Dean numbers, secondary vortices appear and promote chaotic advection [8,9]. This type of mixer is efficient at intermediate Reynolds numbers, roughly for 40 < Re < 2000, and is thus not suitable for highly viscous fluids such as the one addressed in the present study.…”