Electro-osmotic heat transfer

Chapter 4 is devoted to single-phase heat transfer. Data on heat transfer in circular micro-tubes and in rectangular, trapezoidal and triangular ducts are presented. Attention is drawn to the effect of energy dissipation, axial conduction and wall roughness on the thermal characteristics of flow. Specific problems connected with electro-osmotic heat transfer in micro-channels, three-dimensional heat transfer in micro-channel heat sinks and optimization of micro-heat exchangers are also discussed. 

The subject of this chapter is single-phase heat transfer in micro-channels. Several aspects of the problem are considered in the frame of a continuum model, corresponding to small Knudsen number. A number of special problems of the theory of heat transfer in micro-channels, such as the effect of viscous energy dissipation, axial heat conduction, heat transfer characteristics of gaseous flows in microchannels, and electro-osmotic heat transfer in micro-channels, are also discussed in this chapter. 

Electro-Osmotic Heat Transfer in a Micro-Channel... 

Mala GM, Li D, Werner C (1997b) Flow characteristics of water through a micro-channel between two parallel plates with electro kinetic effects. Int J Heat Fluid Flow 18 491 96 Male van P, Croon de MHJM, Tiggelaar RM, Derg van den A, Schouten JC (2004) Heat and mass transfer in a square micro-channel with asymmetric heating. Int J Heat Mass Transfer 47 87-99 Maranzana G, Perry I, Maillet D (2004) Mini- and micro-channels influence of axial conduction in the walls. Int J Heat Mass Transfer 47 3993 004 Maynes D, Webb BW (2003) Full developed electro-osmotic heat transfer in microchannels. Int J Heat Mass Transfer 46 1359-1369... 

Maynes, D. and Webb, B.W., Fully Developed Electro-Osmotic Heat Transfer in Microchannels, Int. J. Heat Mass Transfer, 2003, 46, 1359-1369. 

Maynes D., B. W. Webb, 2003, Fully-developed electro-osmotic heat transfer in microchannels, Int. J. Heat and Mass Transfer, 46, 1359-1369. 

Maynes D, Web BW (2004) The effect of viscous dissipation in thermally fully-developed electro-osmotic heat transfer in microchannels. Int J Heat Mass Transf 47 987-999... 

There may also be a phase change phenomena associated with the motion of water in the membrane nnder a temperature gradient, since Bradean et al. [22] showed an exponential relationship between liqnid flnx and the temperature gradient and heat flux, but the exact nature of this is not fully understood. This mode of transport has not commonly been inclnded in the analysis of normal operation, since this effect is obscnred by the net diffusive and electro-osmotic drag transfer. Under startup or shutdown conditions, however, where larger gradients in temperature can exist, the net water flux from this mode can be significant, and has been exploited to passively drain the DM on shutdown to a frozen state [22]. 

A general case of heat transfer under the conditions of combined action of electro-osmotic forces and imposed pressure gradient was considered by Chakra-borty (2006). The analysis showed that in this case the Nusselt number depends not only on parameters z and S, but also on an additional dimensionless group, which is a measure of the relative significance of the pressure gradient and osmotic forces. 

The fully developed velocity distribution in micro parallel plate channel and micro tube are well known [19]. Using a fully developed velocity one could investigate thermally developing heat transfer and its limiting case - thermally developed heat transfer. The corresponding solutions for electro-osmotic flow in micro parallel plate channel and micro tube are special cases from the general results given in the book by [20]. 

Thermally fully developed heat transfer do to electro-osmotic fluid transport in micro parallel plate channel and micro mbe has been recently investigated by [21]. The dimensionless temperature profile and corresponding Nusselt number have been determined for imposed constant wall heat flux and constant temperature. The complement paper [22] study the effect of viscous dissipation. These two papers gives important physical details and references. The analyses of both papers is based on the classical simplifying assumptions that are avoided in the book by Mikhailov and Ozisik [20]. 

Consider the heat transfer in thermally and hydrodynamically developed electro-osmotic flow inside a micro conduits under following assumptions ... 

Both designs for the annular electrochromatograph appear to be limited by heat transfer (79) and to suffer from mechanical and electro-osmotic dispersion of the solute bands. However, electro-osmosis may actually decrease dispersion under some conditions, according to a model developed by Yoshisato and co-workers (98). Precise and comprehensive models of annular electrochromatography, now under development, are necessary to guide the design and operation of the equipment. 

Some use has been made of Teflon as it is ultraviolet transparent and also exhibits significant electro-osmotic flow. However, it is difficult to form tubing with a regular and precise internal diameter and it also suffers from adsorptive problems and poor heat transfer characteristics. 

This condition is particularly appropriate to analyze the convective heat transfer for electro-osmotic flows for which the velocity tends to become uniform on the cross-section. 

Convective Heat Transfer in Microchanneis, Figure 5 Nusselt numbers as a function of the electro-osmotic diameter (kD[ ) for rectangular microchanneis. The filled symbols denote an aspect ratio 8 = 0.25, whereas the open symbols are for 8 = O.SO.The superscript sf stands for slug flow ... 

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