Fully-Developed Thermal Transport in Combined Pressure and Electro-Osmotically Driven Flow in Microchannels

Thermally fully-developed heat transfer has been analyzed for combined electro-osmotic and pressure driven flow in a circular microtube. The two classical thermal boundary conditions of constant wall heat flux and constant wall temperature were considered. Such a flow is established by the combination of an imposed pressure gradient and voltage potential gradient along the length of the tube. The induced flow rate and velocity profile are functions of the imposed potential gradient, electro-osmotic mobility of the fluid, the ratio of the duct radius to the Debye length, the established streamwise pressure gradient, and the fluid viscosity. The imposed voltage gradient results in Joule heating in the fluid, with an associated distributed volumetric source of energy. For this scenario, the solution for the fully developed, dimensionless temperature profile and corresponding Nusselt number have been determined. The fully-developed Nusselt number is found to depend on the duct radius/Debye length ratio (termed the relative duct radius), the dimensionless volumetric source, and a dimensionless parameter that characterizes the relative strengths of the two driving mechanisms. This parameter can take on both positive and negative values, depending on the signs of the streamwise voltage and pressure gradients imposed. Analytical results are presented and discussed for a range of the governing dimensionless parameters.