Chaotic heat transfer in a periodic two-dimensional flow

Abstract

Chaotic heat transfer in the annular region between two confocal ellipses is analyzed with tools developed in previous mixing studies as well as specific ones presented here. In particular, we show that even though the Eulerian temperature field is periodic, the Lagrangian temperature of a particle can be either periodic or chaotic depending on its initial position. A potential mixing zone, very similar to the one defined by Kaper and Wiggins, is defined for modulated heteroclinic trajectories. The geometry and modulation protocol can be optimized so that a greater than 100% increase of heat transfer over that of conduction is obtained.

Mass transfer to reactive boundaries from steady three-dimensional flows in microchannels

“…1,[14][15][16][17][18][19][20][21][22][23] Heat transfer has been studied in more detail than mass transfer in these systems; this work tends to consider a low Pe regime due to the high diffusivity of heat, but it is otherwise analogous to questions of mass transfer. Chang and Sen have identified two distinct classes of transfer: 8 transfer of solute from one boundary to another across the flow 14,[16][17][18][19] and transfer of solute between the bulk and the wall ͑i.e., to fill or empty the solute from the bulk͒; 1,15,[20][21][22][23] our study falls into the category of bulk-to-wall transfer. Studies have also considered transfer to slip [14][15][16][17][18][19] and no-slip 1,[20][21][22][23] boundaries; our choice of reactor geometry simulates a no-slip reactive boundary.…”

“…Chang and Sen have identified two distinct classes of transfer: 8 transfer of solute from one boundary to another across the flow 14,[16][17][18][19] and transfer of solute between the bulk and the wall ͑i.e., to fill or empty the solute from the bulk͒; 1,15,[20][21][22][23] our study falls into the category of bulk-to-wall transfer. Studies have also considered transfer to slip [14][15][16][17][18][19] and no-slip 1,[20][21][22][23] boundaries; our choice of reactor geometry simulates a no-slip reactive boundary. Analysis of rates of transfer have been performed in the entrance region ͑small axial distance͒ and in the asymptotic region ͑large axial distance͒, and results have been quoted for various quantities such as the flux, transfer coefficient, efficiency, or effective diffusivity.…”

Cooling of a Magmatic System Under Thermal Chaotic Mixing

“…The presence of chaotic behaviors in igneous systems is widely reported in literature (e.g., BERGANTZ 2000;PETRELLI et al 2011;PERUGINI and POLI 2012;, but surprisingly, there are few contributions addressing the thermal behavior of a magmatic body experiencing chaotic dynamics. Since the late 1990s, different works on thermal advection of 1 high-viscosity fluids have shown that temperature fields can be strongly modulated by the onset of chaotic dynamics (SAATDJIAN and LEPREVOST 1998;LEFEVRE et al 2003;MOTA et al 2007;EL OMARI and LE GUER 2010a;LE GUER and EL OMARI 2012), but they are mostly confined to industrial processes. Therefore, study of the thermal evolution of a magmatic body in a chaotic environment could be of great interest and would start to fill the gap in previous and recent literature.…”

Chaotic Advection for Thermal Mixing

“…When heat transfer enhancement is involved, two main classes of ow geometries are encountered in the production of chaotic mixing: those that use rotating elements as cylinders (De Campos, Perugini, Ertel-Ingrisch, Dingwell, & Poli, 2011;El Omari & Le Guer, 2010a;Ganesan, Bryden, & Brenner, 1997;Ghosh, Chang, & Sen, 1992;Lefevre, Mota, Rodrigo, & Saatdjian, 2003;Mota, Rodrigo, & Saatdjian, 2007Rodrigo, Mota, Lefèvre, & Saatdjian, 2003;Rodrigo, Mota, Rodrigues, & Saatdjian, 2006;Saatdjian & Leprevost, 1998;Saatdjian, Rodrigo, & Mota, 2011) or translating elements (de la Cruz & Ramos, 2006;Speetjens, 2008) and those that use multiple curved ducts (Acharya, Sen, & Chang, 1992Chagny, Castelain, & Peerhossaini, 2000;Kumar, Mridha, Gupta, & Nigam, 2007;Lasbet, Auvity, Castelain, & Peerhossaini, 2006;Lemenand & Peerhossaini, 2002;Peerhossaini, Castelain, & Le Guer, 1993;Yamagishi, Inaba, & Yamaguchi, 2007). When heat transfer enhancement is involved, two main classes of ow geometries are encountered in the production of chaotic mixing: those that use rotating elements as cylinders (De Campos, Perugini, Ertel-Ingrisch, Dingwell, & Poli, 2011;El Omari & Le Guer, 2010a;Ganesan, Bryden, & Brenner, 1997;Ghosh, Chang, & Sen, 1992;Lefevre, Mota, Rodrigo, & Saatdjian, 2003;Mota, Rodrigo, & Saatdjian, 2007Rodrigo, Mota, Lefèvre, & Saatdjian, 2003;Rodrigo, Mota, Rodrigues, & Saatdjian, 2006;Saatdjian & Leprevost, 1998;Saatdjian, Rodrigo, & Mota, 2011) or translating elements …”