Thermally developing, electro-osmotically generated flow has been analyzed for a circular microtube under imposed constant wall temperature (CWT) and constant wall heat flux (CHF) boundary conditions. Established by a voltage potential gradient along the length of the microtube, the hydrodynamics of such a flow dictate either a slug flow velocity profile (under conditions of large tube radius-to-Debye length ratio, a/lambda_d) or a family of electro-osmotic flow (EOF) velocity profiles that depend on a/lambda_d. The imposed voltage gradient results in Joule heating in the fluid with an associated volumetric source of energy. For this scenario coupled with a slug flow velocity profile, the analytical solution for the fluid temperature development has been determined for both thermal boundary conditions. The local Nusselt number for the CHF boundary condition is shown to reduce to the classical slug flow thermal development for imposed constant wall heat flux, and is independent of Joule heating source magnitude. For the CWT boundary condition, a local minimum in the streamwise variation in local Nusselt number for moderate positive dimensionless inlet temperature is predicted. For negative dimensionless inlet temperature, which arises if the fluid entrance temperature is below the tube wall temperature, the fluid is initially heated, then cooled, resulting in a singularity in the local Nusselt number at the axial location of the heating/cooling transition. The thermal development length is considerably larger than for traditional pressure-driven flow heat transfer, and is a function of the magnitudes of Peclet number and dimensionless inlet temperature. For the EOF velocity profile scenario, numerical techniques were used to predict the fluid temperature development for both wall boundary conditions by utilizing a finite control volume approach. In addition to Joule heating as an energy source, viscous dissipation is also considered. The results predict that for decreasing a/lambda_d, the local Nusselt number decreases for all axial positions and the thermal development shortens for both wall boundary conditions. Viscous dissipation has significant effect only at intermediate values of a/lambda_d. Results predict local Nusselt numbers to increase for a CWT boundary condition and to decrease for an imposed constant wall heat flux with increasing viscous dissipation.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





electro-osmosis, electro-osmotic, heat transfer, numerical heat transfer, convection, thermally developing, microchannel, microtube, slug flow