Analytical solutions of Nusselt number for thermally fully developed flow in microtubes under a combined action of electroosmotic forces and imposed pressure gradients

Abstract

Closed form expressions are developed for Nusselt number variation in a thermally fully developed microtube flow, under a combined influence of electroosmotic forces and imposed pressure gradients. The analysis takes care of the interaction amongst pressure driven convection and Joule heating effects, in order to obtain the pertinent rate of heat transfer. While separate limiting conditions on the asymptotic Nusselt number can be obtained for pure electroosmotic and solely pressure driven flows, relative influences of electrical potential gradients and imposed pressure gradients acting in tandem are also critically analyzed, as a function of the tube radius normalized with respect to the Debye length. Significant insights are also developed regarding the influence of adverse pressure gradients on the thermal transport, in presence of aiding electroosmotic effects.