Thermally developing electroosmotic transport of nanofluids in microchannels

Abstract

A theoretical analysis is presented in this work to assess the influence of nanofluids on thermally developing and hydrodynamically developed electroosmotic transport in parallel plate microchannels (Graetz problem). The hydraulic diameters of the microchannels are assumed to be beyond a certain threshold limit, so that the electric double layers formed adjacent to the plates do not overlap with each other. The volumetric heating arising from the conduction currents in the flow is modeled using Ohm’s law. The viscous generation terms in the energy equation are neglected, based on the earlier findings that the consequent effects are negligible as compared to the Joule heating effects in electroosmotically driven microchannel flows. Closed form expressions for the pertinent temperature distributions and the Nusselt number variations are obtained by employing the method of separation of variables in conjunction with an eigen value formulation, in order to assess the influence of volume fraction of the dispersed nano-particles on the overall rates of convective transport. It is revealed that the effects of nano-particles in the fluid turn out to be significant in the thermal entrance region only, especially for higher Peclet number values. The implications of the incorporation of nanofluids are demonstrated to be somewhat non-trivial in nature, and are strongly determined by the effective Peclet number values obtained on the basis of the phase-integral values of the thermo-physical properties and the pertinent flow parameters.