Thermally Developing Electroosmotic Convection in Rectangular Microchannels with Vanishing Debye-Layer Thickness

摘要

Thermally developing electroosmotically generated flow in rectangular ducts has been analyzed for the constant-wall-temperature boundary condition. In such flow, fluid motion is induced not by an applied pressure gradient, but by an applied electric potential. For fluid-tube-material combinations that yield a Debye layer of vanishing thickness, the velocity distribution is essentially uniform across the duct cross section. In addition, the applied potential gradient induces an electrical current that results in volumetric heating in the fluid. An analytical solution to the hydrodynamically developed, thermally developing transport for such a flow is presented in this paper. The effect of variations in the duct aspect ratio, the relative magnitude of the volumetric generation, and the Peclet number on the thermal transport are explored over the possible ranges of these parameters. The solution reveals a local minimum in the streamwise variation of the local perimeter-averaged Nusselt number for moderate, positive values of tbe dimensionless duct inlet fluid temperature. For negative inlet temperatures, the fluid is initially heated and then cooled, creating a singularity in the local, perimeter-averaged Nusselt number at this transition. Far downstream, heat transport approaches constant-wall-heat-flux conditions for both positive and negative inlet temperatures. The fully developed Nusselt number decreases from a maximum for the parallel-plate configuration to a minimum for the square duct. Electroosmotically generated flow exhibits considerably longer thermal-entry regions than pressure-driven flow, and the development length is observed to be a function of Peclet number, dimensionless inlet temperature, and channel aspect ratio.