The effect of viscous dissipation in thermally fully-developed electro-osmotic heat transfer in microchannels

The influence of viscous dissipation on thermally fully-developed, electro-osmotically generated flow has been analyzed for a parallel plate microchannel and circular microtube under imposed constant wall heat flux and constant wall temperature boundary conditions. Such a flow is established not by an imposed pressure gradient, but by a voltage potential gradient along the length of the tube. The result is a combination of unique electro-osmotic velocity profiles and volumetric heating in the fluid due to the imposed voltage gradient. For large ratio of the microtube radius (or microchannel half-width) to Debye length, the wall-normal fluid velocity gradients can be extremely high, which has the potential for significant viscous heating. The solution for the fully-developed, dimensionless temperature profile and corresponding Nusselt number have been determined for both geometries and for both thermal boundary conditions. It is shown that three dimensionless parameters govern the thermal transport: the relative duct radius (ratio of the duct radius or plate gap half-width to Debye length), the dimensionless volumetric source (ratio of Joule heating to wall heat flux), and a dimensionless parameter that relates the magnitude of the viscous heating to the Joule heating. Surprisingly, it is shown that the influence of viscous dissipation is only important at low values of the relative duct radius. For magnitudes of the dimensionless parameters which characterize most practical electro-osmotic flow applications, the effect of viscous dissipation is negligible.